CBSE Sample Papers for Class 12 Economics Delhi – 2008

Time allowed : 3                                                                                                                                 hours Maximum marks 100

GENERAL INSTRUCTIONS
(i) All questions in both the sections are compulsory.
(ii) Marks for questions are indicated against each.
(iii) Questions No. 1-5 and 17-21 are very short-answer questions carrying 1 nic-k each. They are required to be answered in one sentence each.
(iv) Questions No. 6-10 :dnd 22-26’ar? short-answer questions carrying 3 marks each. Answers to them should normally not exceed 60 words each.
(v) Questions No. 11-13 and 27-29 are also short-answer questions carrying 4 marks each. Answers to them should normally not exceed 70 words each.
(vi) Questions No. 14-16 and 30-32 are long-ansxoer questions carrying 6 marks each. Answers to them should normally not exceed 100 words each.
(vii) Ansivers should be brief and to the point and the above word limit should be adhered to as far as possible.

SET I

SECTION A
Q.l. Give the meaning of opportunity cost.
Ans. Opportunity cost is defined as the value of the benefit that is forgone by choosing one alternative rather than the other.
Or
Opportunity cost of using a given resource is defined as the value of the next best use to which the resource could be put.

Q.2. Define market demand.
Ans. Market demand for a commodity is the sum total of all individual demands for that commodity.

Q.3. What does cost mean in Economics?
Ans. Cost is the expenditure incurred on the production of a commodity. It includes both fixed cost and variable cost.

Q.4. Define revenue.
Ans. Revenue refers to the money receipts of a firm from selling its output.

Q.5. Define market for a good.
Ans. Market is defined as an area where potential buyers and sellers of a commodity come in contact with each other.

Q.6. Explain the central problem of “What to produce”.
Ans. This problem signifies ‘what goods should be produced and in what quantities’. This problem‘arises when due to scarcity of resources we cannot produce each and every tiling that we vVSrif ‘Therefore, a decision is to be taken as to what goods should be produced and in what quantities. In short, we have to see whether we should produce consumer goods or producer goods or defence goods or all the goods in some quantity combination.
So, on the basis of importance of various goods, an economy has to decide which goods should be produced and in what quantities.

Q.7. When price of a good rises from Rs. 5 per unit to Rs. 6 per unit, its demand falls from 20 units td 10 units. Compare expenditures on the good to determine whether demand is elastic or inelastic.
Ans.
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When price rises, the total expenditure qKtiie commodity falls. This inverse relation between pice and total expenditure shows that me demand for the commodity is elastic (i.e., ed > 1).

Q.8. What is the relation between good X and good Y in each case, if with fall in the price of X demand for good Y (i) rises and (ii) falls? Give reason.
Ans. (a) If the fall in the price of commodity X leads to a rise in the demand for good Y, then X and Y are complementary goods which means they are used with each other for the satisfaction of same want, e.g., bread and butter.
(b) In case of fall in the price of commodity X leads to a fall in demand for commodity Y, then the commodities X and Y are substitutes for each other, i.e., they can be used in place of each other for the satisfaction of same want, e.g., tea and coffee.

Q.9. Explain the effect of technical progress on the supply of a good.
Ans. Technical progress leads’ to an increase in the supply of a commodity, i.e., at the same price more quantity is supplied during a given period. In such a case, as shown in Diagram 1, a rightward shift: takes place in the supply curve.
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Explain the effect of rise in input prices on the supply of a good.
Ans. Rise in the price of inputs will lead to a decrease in the supply of a good which means that at the same price lesser quantity will be offered for sale during a period of time.
Graphically, it can be shown as leftward shift in the supply curve, as shown in Diagram 2.

Q.10. State three features of monopoly.
Ans. Three features of monopoly are:
(i) Single seller of a commodity. This irieans the firm and industry are one and the same,
(ii) No close substitutes. The product offered for sale by the monopolist has no competition from other products.
(iii) No entry of firms, i.e., new firms cannot enter this market.

Q.11. Explain the conditions leading to maximisation of profits by a producer. Use total cost and total revenue approach.
Ans. Producer’s equilibrium means that combination of price and quantity of;Output tyhich yields maximum profit. Under total revenue and total cost approach, produces equilibrium refers to the stage of output level where the difference between TR and TCJ is maximum and total profits fall as more units of output are produced.
The two essential conditions are:
(i) The difference between TR and TC is maximum.
(ii) Total profits fall if output increases beyond equilibrium output ,h . TC Producer’s equilibrium can graphically be shown taking the example of perfect competition.TR is a 45° straight line since AR (price) is constant. TC is total cost curve.
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At OQ level of output, profit i.e. the gap between AR and AC is maximum. This is the point of producer’s equilibrium. Output beyond OQ level, will reduce the total profit.

Note: This example relates to perfect competition.

Q.12. Complete the following table:
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Ans.
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Q.13. Complete the following table:
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Ans.
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(or)
Complte the following table?
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Ans.
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Q.14. A consumer cbriShmes dhly two goods. Explain his equilibrium with tire help of utility approach.
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Ans. A consumer is in a state of equilibrium when he spends his given income on purchase of a commodity (or combination of goods) in such a way that gives him maximum satisfaction. In case of two commodities, consumer attains equilibrium when

Here MUj and MUy = Marginal utilities of x and y respectively.
Px and Py are prices of x and y.
MUm is marginal utility of money.
This implies that a consumer attains equilibrium, (rnaximum satisfaction) when the marginal utility obtained from the last rupee spent on both goods becomes equal. This is known as the law of Equi-Marginal Utility.

Q.15. Explain the Law of Variable Proportions through the behaviour of both Total Product and ’Marginal Product. Give reasons.
Ans. The law of variable proportions explains the relationship between inputs and outputs in the short run. In die short run, some factors of production (inputs) are fixed and other factors inputs are variable. The quantity of output can be increased by increasing the use of variable input.
As more and more units of variable input are employed, the proportion between the fixed and variable factors keeps on changing. The output passes through three phases. These three phases are identified with respect to the marginal product.
Phase I: TP increases at an increasing rate. The first phase of production lasts till the marginal product keeps rising and reaches its highest point. This is the phase of Increasing Returns to a factor and during this phase, total product increases at an increasing rate.
Phase II: TP increases at a diminishing rate. In this phase, Marginal Product is declining, but is positive. In this phase total product increases but at a diminishing rate. This phase ends when Marginal Product is zero and Total Product is at its maximum level. A producer always operates in this stages.
Phase III: TP is falling. In this third phase of production, Marginal Product is declining and is negative. Here total product starts falling.
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These phases are shown graphdally in Diagram 4.
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The reasons for the Operation of the Law are:
1. Optimum combination of factors. The phase of increasing marginal product is due to optimum combination of facto* that is required for any given technology, therefore fixed factors get better utilised.
2. However, when more and more units of variable factors are employed to a fixed factor, the fixed factor cannot absorb it and there is overcrowding of variable factors due to which the marginal product falls and becomes negative. This is the phase of diminishing marginal product.

Q.16. Market for a good is in equilibrium. What is the effect on equilibrium price and quantity if both market demand and market supply of the good increase in the same proportion? Use diagram.
Ans. Market for a good will be in equilibrium when quantity demanded and supplied are equal. However, when supply and demand change, changes take place in the equilibrium price and quantity according to the changes in the supply and demand. In the given example, both
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demand and supply change equally. Thus, as shown in the Diagram) both demand and supply curves shift towards right by equal distance. Initially, the point of equilibrium was E and now in the changed situation it is F. The pricti remains die same, i.e., OP, but equilibrium quantity increases from OQ to OQ1.

For Blind Candidates only in lieu of Q. No. 16
Q.16. Market for goods is in equilibrium. What is the effect on equilibrium price and quantity, if both market demand and market supplyrofthe good increase in the same proportion. Use schedule.
Ans.
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The new equilibrium price will be the fiapte,..i.e., Rs.7, but the equilibrium quantity will increase from 16 to 18 units.

SECTIONS
Q.17. Give meaning 6^ uivolu^taiy unemployment
Ans. In an economy wKen all able persons, who are willing to work at the prevailing wage rate, do not get ,w6fk and are unemployed, it is called involuntary unemployment.

Q.18. Define inflktlbnary gap.
Ans. Inflationary gap is a situation when aggregate demand is greater than die aggregate supply at the full ferriployinent level.

Q.19. What is a central bank?
Ans. Central bank’M#te apex institution in the banking structure of a country that manages a state’s currently, money supply, interest rates and oversees the commercial banking system.

Q.20. State any one objective of government budget.
Ans. One objective asf government budget is reallocation of resources for efficient utilisation of government resources and maximising social benefits.

Q.21. Define flexible exchange rate system.
Ans. The foreign exchange rate which is determined by the forces of demand for and supply of the foreign exchange is known as flexible exchange rate.

Q.22. Calculate ‘Value of Output7 from the following data:
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Ans. Value of Output = NVAFC + IC + Depredation + Net Indirect taxes
= (i) + (ii) + (v) + {(iii) – (iv)}
= 100 + 75 + 10 + (20 – 5) = 185 + 15 = Rs. 200 lakhs.

Q.23. “When Exchange Rate of foreign currency rises, its supply rises. How Explain?
Ans. There is direct relationship between foreign exchange rate and its supply This means higher the exchange rate, higher will be the supply of foreign exchange. As sueb, when exchange rate of foreign currency rises, its supply also rises because the Indian rupee (home currency) becomes relatively cheaper in terms of the foreign currency. This encourages exports of Indian goods and ensures more supply of foreign exchange in the market.

Q.24. State components of the current account of Balance of Payments Account. 3
Ans. Components of the Current Account of Balance of Payments Account are:
(i) Export and import of goods (visibles)
(ii) Export and import of services (invisibles)
(iii) Transfer receipts and payments, such-fts gifts and unilateral payments or receipts
(iv) Investment income.

Q.25. What is bank rate policy? How does it work as a method of credit control?
Ans. Bank Rate is the rate of interest which central bank charges from commerdal banks for giving them loans.
There is direct relationship between bank rate and rate of interest, |but the relationship between rate of interest and demand for creditJs inverse.Thus, when volume of credit is to be reduced, bank rate is increased. On the other hand, when volume of credit is to be increased, bank, rate is reduced. In the aforesaid manner, bank rate is used for controlling the volume of credit.
(or)
What are open market operations? How dcrthese work as a method of credit control?
Ans. Open market operations refer to the purchase and sale of government securities in the open market by the central bank.
The functioning of this method is like this: When central bank of the country wants to increase the volume of credit, it starts purchasing securities from the market. These securities are generally bought at a higher price than the market price. As such, banks start selling them, as a result of which their cash reserves increase, i.e., their liquid assets increase. As a result of this, banks now can create more credit. On the contrary, when central bank wants to control the volume of credit, it starts selling securities in the market which are bought by the commercial banks. With the result, their cash reserves are reduced and this adversely affects their power of creating credit.

Q.26. Give meaning of capital receipts and revenue receipts with an examine of each.
Ans. Capital receipts are those receipts which are created either by incurring a liability or by disposing off assets, such as public debt, disinvestment, etc. Revenue Receipts are those receipts which do not create any asset or liability or which do not reduce assets, such as tax revenue.

Q.27. As a result of increase in investment by Rs. 125 crores, National Income increases by Rs. 500 crores. Calculate marginal propensity to consume.
Ans.
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Q.28. Give four agency functions of commercial banks.
Or
Explain the acceptance of deposits function of commercial banks.
Ans.(Out of Syllabus for 2011 examination and onwards)

Q.29. What is fiscal deficit? What are its implications?
Ans. Fiscal deficit refers to the excess of total expenditure over total receipts (excluding borrowings) during the given fiscal year.
Implications of Fiscal Deficit are as follows:
(1) Debt trap: As fiscal deficit indicates, the total borrowing requirements of the government include both, i.e., repayment of the principal amount and also the payment of interest.
It increases the revenue expenditure in the form of interest payment leading to revenue deficit. This ultimately creates a vicious circle of fiscal and revenue deficit forcing the government to take more loans to service and settle the previous loans.
(2) Inflation: For meeting the borrowing requirements, file government may borrow from the Reserve Bank of India. When RBI prints new currency to meet the deficit requirements, it increases the rribney supply in the economy and creates inflationary pressure.
(3) Reduces future growth: The debt and financial burden of interest payments bn the . revenue expenditure causes a reduction on the capital expenditure for growth and development of the economy.
(4) Foreign dependence: In case fire government borrows from the rest of the world, then dependence of the country on other countries increases and it may not augur well for its prestige.

Note: Points (3) and (4) are not included in the present syllabus

Q.30. Calculate ‘Net Domestic Product at Factor Cost and Gross National Disposable Income from the following data:
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Ans.NDP at\( { F }_{ c }\)
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Q.31. Explain determination of equilibrium level of income using ‘consumption plus investment’ approach. Use diagram.
Ans. ‘Consumption plus Investment’ approach determining the equilibrium level of income is the Aggregate Demand and Aggregate Supply Approach. According to this approach, the equilibrium level of income.is determined at a point where aggregate demand and aggregate supply are equal.
Aggregate Demand (AD). It represents total expenditure in an economy. Consumption expenditure and investment expenditure are its main components. Consumption is a function of income but there is autonomous consumption expenditure also, i.e., consumption at zero level of income.
In the table given below, consumption expenditure is shown in Column II. Investment expenditure is autonomous and is the same at all levels of income. In Column III, investment expenditure is shown. Adding Column II and Column III, we get aggregate demand shown in Column IV.
Aggregate Supply is the value of goods and services produced is equal to National Income. It is shown in Column V.
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The equilibrium level of income will be 300 because at this level AD and AS are equal.
According to Diagram 6, the equilibrium level of income will be OQ, because at this level AD and AS are equal.

Q.32.Explain the determination of equilibrium level of income using ‘saving-investment approach’. Use diagram
Ans. At the equilibrium level of income, aggregate demand is equal to aggregate supply, and saving is equal to investment. Saving is that part of income which is not consumed. By investment we mean physical investment i.e., creation of physical investment like machines, buildings, etc. Savers and investors are different persons. Those who save are not necessarily those who invest. Savings are done in small amounts and investments are made in huge amounts. Therefore, it is possible that the amount which savers save, may not be the same amount which investors want to invest. It means planned saving may not be equal to planned investment but actual saving is always equal to actual investment.
According to the table (on the next page), the equilibrium level of income rate will be 300, because at this level saving and investment are equal. At any other level of income, either saving is more than investment or less than investment.
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According to Diagram 7, saving and investment curves intersect each other at point E, when the level of income is OQ.

For Blind Candidates only in lieu of
Q. No. 31 Explain determination of equilibrium level of income using consumption plus investment approach. Use schedule.
Or
Explain determination of equilibrium level of income using savings-investment approach. Use schedule.
Ans. Both the questions have been answered above. But blind candidates do not have to draw diagrams.

Q.32. Giving reasons explain how the following are treated while estimating national income:
(i) Payment of fees to a lawyer engaged by firm.
(ii) Rent free house to an employee by an employer.
(iii) Purchases by foreign tourists.
Ans. (i) It is an intermediate expenditure by the firm hiring the services of a lawyer, hence it will not be included in the National Income.
(ii) It is included in the National Income as compensation of employees.
(iii) It is included, as purchases by foreign tourists generate factor income in the domestic market.

SET II

Note : Except for the following questions,’’all the remaining questions have been asked in Set I.

SECTION A
Q.6. When price of a good falls from Rs. 10 per unit to Rs. 9 per unit, its demand rises from 9 units to 10 units. Compare expenditure on the good to find price elasticity of demand.
Ans.
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With the fall in the price, the total expenditure on the commodity remains unchanged. Therefore \( { E }_{ d }\) = 1 (unitary elastic).

Q.9. State three features of monopolistic competition.
Ans. Features of monopolistic competition are:
1. Large number of sellers selling closely related but not homogeneous products.
2. Product differentiation: The products of the firms are closely related but not perfect substitutes of other firms. There is differentiation in the product on the basis of size, colour, composition, brand, etc.
3. Freedom of entry and exit of firms: The firms can freely enter and exit in this form of market.

Q.10. Explain the central problem of ‘How to produce’.
Ans. The central problem of ‘How to produce’ refers to the choice of the economy in the technique of production. This choice is made because of the difference in the availability of resources. If labour is abundant and cheap, labour intensive technology of production would lead to cost effective production.
In case labour is scarce and costly, capital intensive technology would be used.
For example, cloth can be produced by using more labour (labour intensive technique) as in handloom sector, or cloth can be produced in textile mills using capital intensive technology (i.e., using more machines).

Q.15. Market for a good is in equilibrium. What is the effect on equilibrium price and quantity if the proportionate increase in market demand is greater than increase in market supply. Use diagram.
Ans. When there is increase in demand and supply, both the curves shift towards tight as shown in Diagram 8. DD (demand curve) shifts to D1D1 and supply curve (SS) shifts to SJSJ. Since increase in demand is more than the increase in supply, the shift in DD curve is greater than the shift in SS curve. The initial point of intersection is E, where price is OP and equilibrium of quantity is OQ.
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The new point of intersection is F, where price is OPj and equilibrium output is OQr Thus, in the given situation, both price and equilibrium quantity are greater than the initial position.

SECTION B
Q.17. Define Deflationary Gap.
Ans. Deflationary gap is the excess of aggregate supply over aggregate demand at the full employment level.

Q.21. Give die meaning of full employment
Ans. Full employment refers to the situation in an economy when all the able persons, who are willing to work at the prevailing Wage rate, are fully employed.

Q.26. Calculate ‘intermediate consumption’ from the following data:
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Ans. Intermediate conception.

Q.28. As a result of increase in investment national income rises by Rs. 600 crores. If marginal propensity to consume is 0.75, calculate the increase in investment.
Ans. Given: AY = Rs. 600 crores and MPC = 0.75.
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Q.31. Calculate Gross National Product at market price and Net National Disposable Income from the following data:
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Ans.\( { GNP }_{ MP }\)
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SET III

Note: Except for the following tfuestions, all the remaining questions have been asked in Set I and Set II.

SECTION A
Q.8. State three features of perfect competition.
Ans. Three features of perfect competition are:
1. Large number of buyers and sellers: There are so many buyers and sellers that no individual buyer or seller can influence the price of the commodity in the market.
2. Homogeneous products: Firms in the market supply homogeneous products, i.e., the products are perfect substitutes for each other.
3. Free entry and exit of firms: Firms have the freedom to move in or move out of the industry or the market. There are no barriers to their entry or exit.

Q.9. Explain the central problem of “for whom to produce.”
Ans. The central problem of ‘for whom to produce’ is the problem of distribution of national product among different people eg., rich and poor. This is known as Personal Distribution of the National Product.
‘For whom to produce’ also refers to the functional distribution of National Income to the factors of production -> in lieu of the factor services generated by them, eg., land earns rent, labour earns wages.

Q.10. When price of a good falls from Rs. 8 per unit to Rs. 7 per unit, its demand rises from 12 units to 16 units. Compare expenditures on the good to determine whether demand is elastic or inelastic?
Ans.
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According to total expenditure method when price and total expenditure move in opposite directions, elasticity of demand will be greater than one. In the given example, price and total expenditure are moving in opposite directions, therefore,\( { e }_{ d }\) > 1.

Q.14. Market for a good is in equilibrium. What is the effect on equilibrium price and quantity if increase in market demand is less than increase in market supply? Use diagram. 6
Ans. The market for a good will be in equilibrium when quantity demanded and quantity supplied are equal. In the given question both demand and supply increase.
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With the result, both demand and supply curves will shift to the right. As shown in foe diagram, supply curve will shift from SS to S1S1 and demand curve will shift from DD to DJDJ. Earlier foe point of equilibrium was E and now it is Er Since foe increase in demand is less than foe increase in supply, foe fall in foe price will be less than foe increase in quantity. Thus, as a result of increase in demand and supply both, price will fall , and equilibrium quantity will increase.

SECTION B
Q.20. What is underemployment equilibrium?
Ans. Underemployment equilibrium refers to foe situation in an economy where foe aggregate demand falls short of aggregate supply at full employment.

Q.21. What is consumption function?
Ans. Consumption function refers to -the functional relationship between consumption and National Income.
C =f(Y), where C is Consumption and Y is National Income.

Q.25. Calculate sales from the following data:
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Ans. Gross Value of Output:
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Q.29. If marginal propensity to consume is 0.9, what is the value of multiplier? How much investment is needed to increase national income by Rs. 5000 crores. Calculate.
Ans. MPC = 0.9
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Q.32. Calculate National Income and Net National Disposal Income from the following data:
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Ans.(i)National Income
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(ii) Net National Disposable Income:
NNDI = NNPFC + (Indirext tax – Subsidies) – Net current transfers to abroad = 495 + (30 – 5) —15.= Rs. 505 crores
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NCERT  Exemplar Problems Class 8 Mathematics Chapter 10 Direct and Inverse Proportion

Multiple Choice Questions
Question. 1 Both u and v vary directly with each other. When u is 10, v is 15, which of the following is not a possible pair of corresponding values of u and v?
(a)2 and 3 (b) 8 and 12 (c) 15 and 20 (d) 25 and 37.5
Solution.
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Question. 2 Both x and y vary inversely with each other. When x is 10, y is 6, which of the following is not a possible pair of corresponding values of x and y?
(a) 12 and 5 (b) 15 and 4 (c) 25 and 2.4 (d) 45 and 1.3
Solution.
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Question. 3 Assuming land to be uniformly fertile, the area of land and the yield on it vary
(a) directly with each other
(b) inversely with each other
(c) neither directly nor inversely with each other
(d) sometimes directly and sometimes inversely with each other
Solution. (a) If land to be uniformly fertile, then the area of land and the yield on it vary directly with each other.
Hence, option (a) is correct.
Note Two quantities x and y are said to be in direct proportion, if they increase or decrease together in such a manner that the ratio of their corresponding values remains constant.

Question. 4 The number of teeth and the age of a person vary
(a) directly with each other
(b) inversely with each other
(c) neither directly nor inversely with each other
(d) sometimes directly,and sometimes inversely with each other
Solution. (d) The number of teeth and the age of a person vary sometimes directly and sometimes inversely with each other, we cannot predict about the number of teeth with exactly the age of a person. It change with person-to-person.
Hence, option (d) is correct.

Question. 5 A truck needs 54 litres of diesel for covering a distance of 297 km. The diesel required by the truck to cover a distance of 550 km is (a) 100 litres (b) 50 litres (c) 25.16 litres (d) 25 litres
Solution.
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Question. 6 By travelling at a speed of 48 km/h, a car can finish a certain journey in 10 hours. To cover the same distance in 8 hours, the speed of the car should be
(a) 60 km/h (b) 80 km/h (c) 30 km/h (d) 40 km/h
Solution.
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Question. 7 In which of the following cases, do the quantities vary directly with each other?
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Solution. (a) In option (a),
x = 0.5,2, 8, 32 and y = 2, 8, 32,128
If we multiply x with 4, we get the directly required result as same as shown in corresponding y. In this case, as the value of x increases, the value of y also increases. Hence, option (a) is correct.

Question. 8 Which quantities in the previous question vary inversely with each other?
(a) x and y (b) p and q (c) r and s (d) u and v
Solution.
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Question. 9 Which of the following vary inversely with each other?
(a) Speed and distance covered (b) Distance covered and taxi fare
(c) Distance travelled and time taken (d) Speed and time taken
Solution. (d) We know that, when we increases the speed, then the time taken by vehicle decreases.
Hence, speed and time taken vary inversely with each other.
So, option (d) is correct.

Question. 10 Both x and y are in direct proportion, then \(\frac { 1 }{ x }\) and \(\frac { 1 }{ y }\) are
(a) in indirect proportion
(b) in inverse proportion
(c) neither in direct nor in inverse proportion
(d) sometimes in direct and sometimes in inverse proportion
Solution. (b) If both x arid y are in directly proportion, then \(\frac { 1 }{ x }\) and \(\frac { 1 }{ y }\) are in inverse proportion.
Hence, option (b) is correct.
Note Two quantities x and y are said to be in inverse proportion, if an increase in x cause a proportional decrease in y and vice-versa.

Question. 11 Meenakshee cycles to her school at an average speed of 12 km/h and takes 20 minutes to reach her school. If she wants to reach her school in 12 minutes, her average speed should be (a) 20/3 km/h (b) 16 km/h (c) 20 km/h. (d) 15 km/h
Solution.
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Question. 12 100 persons had food provision for 24 days. If 20 persons left the place, the provision will last for
(a) 30 days (b) 96/5 days (c) 120 days (d) 40 days
Solution.
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Question. 13 If two quantities x and y vary directly with each other, then
(a) \(\frac { x }{ y }\) remains constant (b) x – y remains constant
(c) x + y remains constant ‘ (d)ix y remains constant
Solution. (a) If two quantities x and y vary directly with each other, then \(\frac { x }{ y }\) = k = constant.
Since, in direct proportion, both x and y increases or decreases together such a manner that the ratio of their corresponding value remains constant. Hence, option (a) is correct.

Question. 14 If two quantities p and q vary inversely with each other, then
(a) \(\frac { p }{ q }\) remains constant (b) p + q remains constant (c) p x q remains constant (d) p – q remains constant
Solution. (c) If two quantities p and q vary inversely with each other, then p x q remains constant.
Since, in inverse proportion, an increase in p cause a proportional decrease in q and vice-versa.
Hence, option (c) is correct.

Question. 15 If the distance travelled by a rickshaw in one hour is 10 km, then the distance travelled by the same rickshaw with the same speed in one minute is
(a)\(\frac { 250 }{ 9 }\)m (b)\(\frac { 500 }{ 9 }\)m (c)1000m (d)\(\frac { 500 }{ 3 }\)m
Solution.
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Question. 16 Both x and y vary directly with each other and when x is 10, y is 14,
which of the following is not a possible pair of corresponding values of x and y?
(a) 25 and 35 (b) 35 and 25
(c) 35 and 49 (d) 15 and 21
Solution.
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Fill in the Blanks
In questions 17 to 42, fill in the blanks to make the statements true.
Question. 17 If x = 5y, then x and y vary——— with each other.
Solution.
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Question. 18 If xy = 10, then x and y vary————with each other.
Solution.
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Question. 19 When two quantities x and y are in——-proportion or vary——-they are written as \(x\propto y\)
Solution.When two quantities x and y are in direct proportion or vary directly, they are written as \(x\propto y\) [see definition of direct proportion]

Question. 20 When two quantities x and y are in——-proportion or vary———-they are written as \(x\propto \frac { 1 }{ y }\)
Solution. When two quantities x and y are in inverse proportion or vary inversely, they are written as \(x\propto \frac { 1 }{ y }\) [see definition of inverse proportion]

Question. 21 Both x and y are said to vary——–with each other, if for some positive number k, xy =k.
Solution. Both x and y are said to vary inversely with each other, if for some positive number k,xy = k. [see condition of inverse proportion]

Question. 22 x and y are said to vary directly with each other, if for, some positive number k,———-= k.
Solution. x and y are said to vary directly wifh’ether, if for some positive number k, \(\frac { x }{ y }\)=k.

Question. 23 Two quantities are said to vary——— with each other, if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.
Solution. Two quantities are said to vary directly with each other, if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.

Question. 24 Two quantities are said to vary——–with each other, if an increase in one causes a decrease in the other in such a manner that the product of their corresponding values remains constant.
Solution. Two quantities are said to vary inversely with each other, if increase in one cause a decrease in the other in such a manner that the product of their corresponding values remains constant.

Question. 25 If 12 pumps can empty a reservoir in 20 hours, then time required by 45 such pumps to empty the same reservoir in—-hours.
Solution.
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Question. 26 If x varies inversely as y then
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Solution.
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Question. 27 If x varies directly as y, then
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Solution.
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Question. 28 When the speed remains constant, the distance travelled is——–proportional to the time.
Solution. When the speed remains constant, the distance travelled is directly proportional to the time.
e.g. If 10 km cover in 10 min with uniform speed, then 20 km cover in 20 min with same speed.

Question. 29 On increasing a, b increases in such a manner that \(\frac { a }{ b }\) remains——and positive, then a and b are said to vary directly with each other.
Solution. On increasing a, b increases in such a manner that \(\frac { a }{ b }\) remains constant and positive, then a and b are said to vary directly with each other.

Question. 30 If on increasing a, b decreases in such a manner that—– remains——–and positive, then a and b are said to vary inversely with each other.
Solution. If on increasing a, b decreases in such a manner that ab remains constant and positive, then a and b are said to vary inversely with each other. [see definition of inverse proportion]

Question. 31 If two quantities x and y vary directly with each other, then——— of their corresponding values remains constant.
Solution. If two quantities x and y vary directly with each other, then ratio of their corresponding values remains constant. [see definition of direct proportion]

Question. 32 If two quantities p and q vary inversely with each other, then————- of their corresponding values remains constant.
Solution. If two quantities p and q vary inversely with each other, then product of their corresponding values remains constant.

Question. 33 The perimeter of a circle and its diameter vary—–with each other.
Solution.
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Question. 34 A car is travelling 48 km in one hour. The distance travelled by the car in 12 minutes is ———.
Solution.
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Question. 35 An auto rickshaw takes 3 hours to cover a distance of 36 km. If its speed is increased by 4 km/h, the time taken by it to cover the same distance is———–.
Solution.
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Question. 36 If the thickness of a pile of 12 cardboard sheets is 45 mm, then the thickness of a pile of 240 sheets is——cm.
Solution.
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Question. 37 If x varies inversely as y and x = 4 when y = 6, when x = 3, then value of y is—.
Solution.
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Question. 38 In direct proportion \( \frac { { a }_{ 1 } }{ { b }_{ 1 } }\) —————- \( \frac { { a }_{ 2 } }{ { b }_{ 2 } }\)
Solution.
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Question. 39 In case of inverse proportion,
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Solution.
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Question. 40 If the area occupied by 15 postal stamps is 60 \(c{ m }^{ 2 }\), then the area occupied by 120 such postal stamps will be———.
Solution.
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Question. 41 If 45 persons can complete a work in 20 days, then the time taken by 75 persons will be—–hours.
Solution.
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Question. 42 Devangi travels 50 m distance in 75 steps, then the distance travelled in 375 steps is——– km.
Solution.
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True/False
In questions from 43 to 59, state whether the statements are True or False.
Question. 43 Two quantities x and y are said to vary directly with each other, if for some rational number k, xy =k.
Solution. False
Two quantities x and y are said to vary directly with each other, if \({ x }_{ y }\) = k (constant)

Question. 44 When the speed is kept fixed, time and distance vary inversely with each other.
Solution. False
When the speed is kept fixed, time and distance vary directly with each other.

Question. 45 When the distance is kept fixed, speed and time vary directly with each other.
Solution. False
When the distance is kept fixed, speed and time vary indirectly/inversely with each other. Since, if we increase speed, then taken time will less and vice-versa.

Question. 46 Length of a side of a square and its area vary directly with each other.
Solution. False
Length of a side of a square and its area does not vary directly with each other, e.g. Let a be length of each side of a square.
So, area of the square = \({ Side }^{ 2 }\) = \({ a }^{ 2 }\)
So, if we increase the length of the side of a square, then their area increases but not directly.

Question. 47 Length of a side of an equilateral triangle and its perimeter vary inversely with each other.
Solution. False
Length of a side of an equilateral triangle and its perimeter vary directly with each other, e.g. Let a be the side of an equilateral triangle. So, perimeter = 3 x (Side) = 3 x a = 3a . So, if we increase the length of side of the equilateral triangle, then their perimeter will also increases.

Question. 48 If d varies directly as \({ t }^{ 2 }\), then we can write d\({ t }^{ 2 }\) = k, where k is some constant.
Solution. False
If d varies inversely as \({ t }^{ 2 }\), then we can write d\({ t }^{ 2 }\) = k, where k is some constant.
Since, two quantities x and y are said to be in Inverse proportion, if an increases in x cause a proportional decreases in y and vice-versa, in such a manner that the product of their corresponding values remains constant.

Question. 49 If a tree 24 m high casts a shadow of 15 m, then the height of a pole that casts a shadow of 6 m under similar conditions is 9.6 m.
Solution.
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Question. 50 If x and y are in direct proportion, then (x -1) and (y -1) are also in direct proportion.
Solution.
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Question. 51 If x and y are in inverse proportion, then (x +1) and (y +1) are also in inverse proportion.
Solution. False
If x and y are in inverse proportion, then xy = k (constant) e.g. Let x= 2 and y = 3
.-. xy = 2 x 3= 6. Now, x + 1=2 + 1 = 3 and y+ 1 = 3 + 1 = 4
Then, (x + 1)(y+1) = 3 x 4 = 12 [not in inverse proportion]
Hence, (x+ 1)and (y + 1) cannot be in inverse proportion.

Question. 52 If p and q are in inverse proportion, i.e. pq = k (constant), then (p + 2)and (q – 2) are also in inverse proportion.
Solution. False
If p and q are in inverse proportion, then
xy = k (constant)
e.g. Let p = 3andq = 4
Then, pq = 3×4 = 12
Now, p+ 2 = 3+ 2 = 5 and q-2 = 4-2 =2
(p + 2) (q – 2) = 5 x 2 = 10 [not in inverse proportion]
Henc, (p+2) and (q -2)cannot be in inverse proportion.

Question. 53 If one angle of a, triangle is kept fixed, then the measure of the remaining two angles vary inversely with each other.
Solution.
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Question. 54 When two quantities are related in such a manner that, if one increases, the other also increases, then they always vary directly.
Solution. True
When two quantities are related in such a manner that if, one increases the other also increases, then they always vary directly.
Above statement is correct for direct proportion. It is a basic properties of direct proportion.

Question. 55 When two quantities are related in such a manner that if one increases and the other decreases, then they always vary inversely.
Solution. True
When, two quantities are related in such a manner that if one increases and the other decreases, then they always vary inversely. Above statement is correct for inverse proportion. It is a basic properties of inverse proportion.

Question. 56 If x varies inversely as y and when x = 6, y = 8, then for x = 8, the value of y is 10.
Solution.
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Question. 57 The number of workers and the time to complete a job is a case of direct proportion.
Solution. False
The number of workers and the time to complete a job is a case of indirect proportion, e.g. If 60 workers can complete a work in 10 days.
Then, 120 workers can complete the same work in 5 days.

Question. 58 For fixed time period and rate of interest, the simple interest is directly proportional to the principal.
Solution.
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Question. 59 The area of cultivated land and the crop harvested is a case of direct proportion.
Solution. True
The area of cultivated land and the crop harvested is a case of direct proportion.
Since, the quantities of crop harvested is depend upon area of cultivated land.

In questions 60 to 62, which of the following vary directly and which vary inversely with each other and which are neither of the two ?
Question. 60 (i)The time taken by a train to cover a fixed distance and the speed of the train.
(ii) The distance travelled by CNG bus and the amount of CNG used.
(iii) The number of people working and the time to complete a given work.
(iv) Income tax and the income.
(v) Distance travelled by an auto-rickshaw and time taken.
Solution. (i) The time taken by a train to cover a fixed distance and the speed of the train are inversely proportional. ‘
e.g. Let a train cover 100 km in 1 h with speed 100 km/h.
Then, the same train cover 100 km in 30 min with speed 200 km/h.
(ii) The distance travelled by CNG bus and the amount of CNG used are directly proportional.
e.g. Let a CNG bus can travelled 10 km in 1 kg of CNG.
Then, the same CNG bus travelled 20 km in 2 x 1 = 2 kg of CNG.
(iii) The number of people working and the time to complete a given work are inversely proportional to each other.
e.g. Let 20 workers can complete a work in 1day.
Then, 10 workers can complete the same work in 2 days.
(iv) Income tax and the income are directly proportional to each other, e.g. Let Mr X have 4.5 lakh annual income.
Then, he pay 10% income tax on his income.
But if Mr X have 5.5 lakh annual income, then he has to pay 30% income tax on his salary/income.
(v) Distance travelled by an auto rickshaw and time taken are directly proportional to each other.
e.g. Let an auto rickshaw takes 2 h to travel 10 km.
Then, it will take 4 h to travel 20 km.

Question. 61 (i) Number of students in a hostel and consumption of food.
(ii) Area of the walls of a room and the cost of white washing the walls.
(iii) The number of people working and the quantity of work.
(iv) Simple interest on a given sum and the rate of interest.
(v) Compound interest on a given sum and the sum invested.
Solution.
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Question. 62 (i) The quantity of rice and its cost.
(ii) The height of a tree and the number of years.
(iii) Increase in cost and number of shirts that can be purchased, if the budget remains the same.
(iv) Area of land and its cost.
(v) Sales tax and the amount of the bill.
Solution.(i) The quantity of rice and its cost are directly proportional to each other, e.g. Let 1 kg of rice price = Rs 40
Then, 2 kg of rice price = Rs 2 x 40 = Rs 80
(ii) The height of a tree and the number of years are neither directly nor inversely proportional to each other.
(iii) Increase in cost and number of shirts that can be purchased, if the budget remains the same are inversely proportional to each other, e.g. Let 2 shirts price = Rs 800 After increasing in price of each shirt,
1 shirt price became Rs 800
where budget = Rs 800
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Question. 63 If x varies inversely as y and x = 20 when y = 600, find y when x = 400.
Solution.
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Question. 64 The variable x varies directly as y and x – 80 when y is 160. What is y when x is 64?
Solution.
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Question. 65 l varies directly as m and l = 5, when m =\(\frac { 2 }{ 3 }\) . Find l when m =\(\frac { 16 }{ 3 }\) .
Solution.
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Question. 66 If x varies inversely as y and y =60 when x = 1.5. Find x, when y = 4.5.
Solution.
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Question. 67 In a camp, there is enough flour for 300 persons for 42 days. How long will the, flour last, if 20 more persons join the camp?
Solution.
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Question. 68 A contractor undertook a contract to complete a part of a stadium in 9 months with a team of 560 persons. Later on, it was required to complete the job in 5 months. How many extra persons should he employ to complete the work?
Solution.
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Question. 69 Sobi types 108 words in 6 minutes. How many words would she type in half an hour?
Solution.
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Question. 70 A car covers a distance in 40 minutes with an average speed of 60 km/h. What should be the average speed to cover the same distance in 25 minutes?
Solution.
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Question. 71 It is.given that l varies directly as m.
(a) Write an equation which relates l and m.
(b) Find the constant of proportion (k), when l is 6, then m is 18.
(c) Find l, when m is 33.
(d) Find m, when l is 8.
Solution.
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Question. 72 If a deposit of Rs 2000 earns an interest of Rs 500 in 3 years, how much interest would a deposit of Rs 36000 earn in 3 years with the same rate of simple interest?
Solution.
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Question. 73 The mass of an aluminium rod varies directly with its length. If a 16 cm long rod has a mass of 192 g, find the length of the rod whose mass is 105 g.
Solution.
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Question. 74 Find the values of x and y, if a and b are in inverse proportion.
(a) 12 x 8 (b) 305 y
Solution.
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Question. 75 If Naresh walks 250 steps to cover a distance of 200 metres, find the distance travelled in 350 steps.
Solution.
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Question. 76 A car travels a distance of 225 km in 25 litres of petrol. How many litres of petrol will be required to cover a distance of 540 kilometres by this car?
Solution.
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Question. 77 From the following table, determine if x and y are in direct proportion or not.
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Solution.
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Question. 78 If a and b vary inversely to each other, then find the values of p, q, r; x, y, z and l, m, n.
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Solution.
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Question. 79 If 25 metres of cloth costs Rs 337.50, then
(a) what will be the cost of 40 metres of the same type of cloth? (b) what will be the length of the cloth bought for Rs 810?
Solution.
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Question. 80 A swimming pool.can be filled in 4 hours by 8 pumps of the same type. How many such pumps are required, if the pool is to be filled in 2\(\frac { 2 }{ 3 }\) hours?
Solution.
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Question. 81 The cost of 27 kg of iron is ? 1080, what will be the cost of 120 kg of iron of the same quality?
Solution.
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Question. 82 At a particular time, the length of the shadow of Qutub Minar whose height is 72 m is 80 m. What will be the height of an electric pole, the length of whose shadow at the same time is 1000 cm?
Solution.
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Question. 83 In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel, how long will these provisions last?
Solution.
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Question. 84 Campus and Welfare Committee of school is planning to develop a blue shade for painting the entire school building. For this purpose, various shades are tried by mixing containers of blue paint and white paint. In each of the following mixtures, decide which is a lighter shade of blue and also find the lightest blue shade among all of them.
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If one container has one litre paint and the building requires 105 litres for painting, how many container of each type is required to paint the building by lightest blue shade?
Solution.
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Question. 85 Posing a Question Work with a partner to write at least five ratio statement about this quilt, which has white, blue and purple squares.
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How many squares of each colour will be there in 12 such quilts?
Solution.
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Question. 86 A packet of sweets was distributed among 10 children and each of them received 4 sweets. If it is distributed among 8 children, how many sweets will each child get?
Solution. The total number of children = 10
If each children received 4 sweets, then The total number of sweets = 10 x 4 = 40 sweets
If 40 sweets distributed between 8 children, then each get 40/8 i.e. 5 sweets.

Question. 87 44 cows can graze a field in 9 days. How many less/more cows will graze the same field in 12 days?
Solution.
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Question. 88 30 persons can reap a field in 17 days. How many more persons should be engaged to reap the same field in 10 days?
Solution.
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Question. 89 Shabnam takes 20 minutes to reach her school, if she goes at a speed of 6 km/h. If she wants to reach school in 24 minutes, what should be her speed?
Solution.
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Question. 90 Ravi starts for his school at 8 : 20 am on his bicycle. If he travels at a speed of 10 km/h, then he reaches his school late by 8 minutes but on travelling at 16 km/h, he reaches the school 10 minutes early. At what time does the school start?
Solution.
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Question. 91 Match each of the entries in Column I with the appropriate entry in Column II.
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Solution.
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Question. 92 There are 20 grams of protein in 75 grams of sauted fish. How many grams of protein is in 225 grams of that fish?
Solution.
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Question. 93 Ms Anita has to drive from Jhareda to Ganwari. She measures a distance of 3.5 cm between these village on the map. What is the actual distance between the villages, if the map scale is 1 cm = 10 km?
Solution. The distance between Jhareda to Ganwari in the map = 3.5 cm Given scale, 1 cm = 10 km
So, actual distance between the villages = 35 x 10 = 35 km

Question. 94 A water tank casts a shadow 21 m long. A tree of height 9.5 m casts a shadow 8 m long at the same time. The length of the shadows are directly proportional to their heights. Find the height of the tank.
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Solution.
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Question. 95 The table shows the time four elevators take to travel various distances. Find, which elevator is fastest and which is slowest.
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How much distance will be travelled elevators B and C separately in 140 sec? Who travelled more and by how much?
Solution.
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Question. 96 A volleyball court is in a rectangular shape and its dimensions are directly proportional to the dimensions of the swimming pool given below. Find the width of the pool.
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Solution.
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Question. 97 A recipe for a particular type of muffins requires 1 cup of milk and 1.5 cups of chocolates. Riya has 7.5 cups of chocolates.If she is using the recipe as a guide, how many cups.of milk will she need to prepare muffins?
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Solution.
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Question. 98 Pattern B consists of four tiles like pattern A. Write a proportion involving blue dots and total dots in patterns A and B. Are they in direct proportion? If yes, write the constant of proportion.
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Solution.
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Question. 99 A Fowler throws a cricket ball at a speed of 120 km/h. How long does this ball take to travel distance of 20 m to each the batsman?
Solution.
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Question. 100 The variable x is inversely proportional to y. If x increases by p%, then by what per cent will y decwsose?
Solution. The variable x is inversely proportional to y. xy = k (constant)
Since, we know that two quantities x and y are said to be in inverse proportion, if an increase in * cause a proportional decrease in y and vice-versa.So, we can say y decrease by p%.

Question. 101 Here is a keyboard of a harmonium.
(a) Find the ratio of white keys to black keys on the keyboard.
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(b) What is the ratio of black keys to all keys on the given keyboard?
(c) This pattern of keys is repeated on larger keyboard. How many black keys would you expect to find on a keyboard with 14 such patterns?
Solution.
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Question. 102 The following table shows the distance travelled by one of the new eco-friendly energy-efficient car travelled on gas.
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Which type of properties are indicated by the table? How much distance will be covered by the car in 8 litres of gas?
Solution.On the basis of given table, the distance travelled by one of the new eco-friendly energy-efficient earns travelled on gas.
The car travelled 15 km In 1 L of gas.
The car travelled 7.5 km in 0.5 L of gas.
The car travelled 30 km in 2 L of gas.
This rate shows direct proportion between litres of gas and the distance cover.
The car can cover the distance in 8 L of gas = 8 x 15 = 120 km

Question. 103 Kritika is following this recipe for bread. She realises her sister used most of sugar syrup for her breakfast. Kritika has only \(\frac { 1 }{ 6 } \) cup of syrup,so she decides to make a small size of bread. How much of each ingredient shall she use?
Bread recipe
1 cup quick cooking oats                                                        2 cups bread flour
\(\frac { 1 }{ 3 } \)cup sugar syrup               1 tablespoon cooking oil
1 \(\frac { 1 }{ 3 } \) cups water                    3 tablespoons yeast
1 tablespoon salt
Solution.
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Question. 104 Many schools have a recommended students-teachers ratio as 35:1. Next year, school expects an increase in enrollment by 280 students. How many new teachers will they to appoint to maintain the students-teachers ratio?
Solution.
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Question. 105 Kusum always forgets how to convert miles to kilometres and back again. However, she remembers that her car’s speedometer shows both miles and kilometres. She knows that travelling 50 miles per hour is same as travelling 80 kilometres per hour. To cover a distance of 200 km, how many miles Kusum would have to go?
Solution.
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Question. 106 The student of Anju’s class sold posters to raise money. Anju wanted to create a ratio for finding the amount of money, her class would make for different numbers of posters sold. She knew, they could raise Rs 250 for every 60 posters sold.
(a) How much money would Anju’s class make for selling 102 posters?
(b) Could Anju’s class raise exactly Rs 2000? If so, how many posters would they need to sell? If not, why?
Solution.
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The post NCERT Exemplar Problems Class 8 Mathematics Direct and Inverse Proportion appeared first on Learn CBSE.

NCERT Exemplar Problems Class 8 Mathematics Chapter 9 Comparing Quantities

Multiple Choice Questions
Question. 1 Suppose for the principal P, rate R% and time T, the simple interest is S and compound interest is C. Consider the possibilities
(i) C>S
(ii) C = S
(iii) C <S Then,
(a) only (i) is correct (b) either (i) or (ii) is correct
(c) either (ii) or (iii) is correct (d) only (iii) is correct
Solution. (a) Let the principal (P) = Rs. 100
Rate of interest (R) = 100% and time period (T) = 2 yr
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Question. 2 Suppose a certain sum doubles in 2 yr at r% rate of simple interest per annum and R°/o rate of interest per annum compounded annually. Then,
(a) r < R (b) R<r
(c)R = r (d) Cannot be determined
Solution. (b) If the total amount received after 2 yr is same for both simple interest and compound interest on same principal, then the rate of simple interest is greater than the rate of compound interest.
i.e.R<r
Hence, option (b) is correct.

Question. 3 The compound interest on Rs. 50000 at 4% per annum for 2 yr compounded annually is (a) Rs. 4000 (b) Rs. 4080 (c) Rs. 4280 (d) Rs. 4050
Solution. (b) Given, principal (P) = Rs. 50000
Rate of interest (R%) = 4% per annum
Time period (T) = 2 yr We know that,
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Question. 4 If marked price of an article is Rs. 1200 and the discount is 12%, then the selling price of the article is (a)Rs. 1056 (b) Rs. 1344 (c) Rs. 1212 (d)Rs.1188
Solution. (a) Given, marked price of an article = Rs. 1200 Discount % = 12%
Discount = Discount % on marked price
= A x 1200=12 x 12 = Rs.144
Selling price = Marked price – Discount Selling price = Rs.11200 – Rs. 144 = Rs.1056 Hence, option (a) is correct.

Question. 5 If 90% of x is 315 km, then the value of x is
(a) 325 km (b) 350 km (c) 350 m
Solution. (b) We have, 90% of x = 315 km
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Question. 6 To gain 25% after allowing a discount of 10%, the shopkeeper must mark the price of the article which cost him Rs. 360 as
(a) Rs. 500 (b) Rs. 450 (c) Rs. 460 (d) Rs. 486
Solution. (a) Let the marked price of the article be Rs.x.
Cost price of the article = Rs. 360 According to the question,
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Question. 7 If a% is the discount per cent on marked price x, then discount is
(a)\(\frac { x }{ a } \)x 100 (b) \(\frac { a }{ x } \) x 100
(c) x x \(\frac { a }{ 100 } \) (d)\(\frac { 100 }{ xa } \)
Solution. (c) Since, discount can be calculated always on marked price, when discount percentage is given. Discount = Discount % on marked price = \(\frac { a }{ 100 } \)x x
Hence, option (c) is correct.

Question. 8 Ashima took a loan of Rs. 100000 at 12% per annum compounded half-yearly. She paid Rs. 112360. If (1.06)2 is equal to 1.1236, then the period for which she took the loan is
(a) 2 yr (b) 1 yr
(c) 6 months (d) 1 \(\frac { 1 }{ 2 } \) yr
Solution. (b) Given, principal (P) = Rs.100000
Rate of interest (R%) = 12% per annum compounded half-yearly Let m be the time period, v Amount paid = Rs.112360
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Question. 9 For calculation of interest compounded half-yearly, keeping the principal same, which one of the following is true?
(a) Double the given annual rate and half the given number of years
(b) Double the given annual rate as well as the given number of years
(c) Half the given annual rate as well as the given number of years
(d) Half the given annual rate and double the given number of years
Solution. (d)If interest is compounded half-yearly, then R=\(\frac { R }{ 2 } \) and T=2T=2n
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So, half the given annual rate and double the given number of years. Hence, option (d) is correct.

Question. 10 Shyama purchases a scooter costing Rs. 36450 and the rate of sales tax is 9%, then the total amount paid by her is
(a) Rs. 36490.50 (b) Rs. 39730.50
(c) Rs. 36454.50 (d) Rs. 33169.50
Solution.  (b) Since, sales tax is charged on the sale of an item by the government and is added to the bill amount. Shyama purchase a scooter of costing = Rs. 36450 Sales tax paid =9%
So, total amount paid by her
= Rs. 36450 of 9%+ Rs. 36450
= \(\frac { 9 }{ 100 } \)x36450 + 36450
= 9 x 364.5 + 36450 = 3280.5 + 36450 = Rs. 39730.5
Hence, option (b) is correct.

Question. 11 The marked price of an article is Rs. 80 and it is sold at Rs. 76, then the discount rate is
(a) 5% (b) 95%
(c) 10% (d) approx 11 %
Solution. (a) The marked price of an article = Rs. 80 Sold price of the article = Rs. 76 We know that,
Selling price = Marked price – Discount Discount = Marked price – Selling price
=> Discount = Rs.80-Rs.76 = Rs.4
Discount % = \(\frac { 4 }{ 80 } \) x 100= \(\frac { 40 }{ 80 } \) = 5%
Hence, option (a) is correct.

Question. 12 A bought a tape recorder for Rs. 8000 and sold it to B. B in turn sold it to C, each earning a profit of 20%. Which of the following is true?
(a) A and B earn the same profit (b) A earns more profit than B
(c) A earns less profit than<5 (d) Cannot be determined
Solution. (c) Cost price of tape recorder for/4 = Rs.8000
Cost price of tape recorder for B =20% profit on cost price for A
=\(\frac { 20 }{ 100 } \) x 8000 + 8000
=20 x 80 + 8000
=1600 + 8000=Rs.9600
Cost price of tape recorder for C=20% profit on cost price for B
=\(\frac { 20 }{ 100 } \) x 9600 + 9600
=1929 + 9600=Rs.11520
Here, profit for A= Rs.1600 Profit for B = Rs.1920
So, A earns less profit than B.
Hence, option (c) is correct.

Question. 13 Latika bought a teapot for Rs. 120 and a set of cups for Rs. 400. She sold teapot at a profit of 5% and cups at a loss of 5%. The amount received by her is
(a) Rs. 494 (b) 7 546
(c) Rs. 506 (d) Rs. 534
Solution. (c) Latika bought a teapot = Rs. 120 and a set of cups = Rs. 400 She sold teapot at a profit of 5%,  So, selling price of teapot =\(\frac { 5 }{ 100 } \) x 120 + 120
= \(\frac { 120 }{ 20 } \) +120
= 6 + 120 = Rs.126 Also, she sold cups at a loss of 5%.
So, selling price of cups = 400 –\(\frac { 5 }{ 100 } \) x 400
= 400 – 20 = Rs. 380
Then, the total amount received by her = Rs. 126 + Rs. 380 = Rs. 506 Hence, option (c) is correct.

Question. 14 A jacket was sold for Rs. 1120 after allowing a discount of 20%. The marked price of the jacket is
(a) Rs. 1440 (b) Rs. 1400 (c) Rs. 960 (d) Rs. 866.66
Solution. (b) Let the marked price of the jacket be Rs. x.
Discount % on marked price = 20%
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Question. 15 A sum is taken for two years at 16% per annum. If interest is .compounded after every three months, the number of times for which interest is charged in 2 yrs is
(a) 8 (b) 4 (c) 6 (d) 9
Solution. (a) Since, rate of interest is calculated after every three months. Similarly, the time period for amount in a year will 4 times.
If amount is taken for 2 yr, means 4×2 = 8 times charged in 2 yr.
Hertee, option (a) is correct.

Question. 16 The original price of a washing machine which was bought for Rs. 13500 including of 8% VAT, is
(a) Rs. 12420 (b) Rs. 14580 (c) Rs.12500 (d) Rs. 13492
Solution. (a) The price of the washing machine = Rs.13500
VAT [Value Added Tax] is included in selling price, which is 8%.
The original price of the washing machine including of 8% VAT
= 13500-13500 x \(\frac { 8 }{ 100 } \)
= 13500-135 x 8 = 13500-1080= Rs.12420 Hence, option (a) is correct.

Question. 17 Avinash bought an electric iron for Rs. 900 and sold it at a gain of 10%. He sold another electric iron at 5% loss which was bought
Rs. 1200. On the transaction, he has a
(a) profit of Rs. 75 (b) loss of Rs. 75 (c) profit of Rs. 30 (d) loss of Rs. 30
Solution. (c) Avinash bought an electric iron = Rs. 900 He sold it, at 10% profit.
So, selling price of the electric iron = \(\frac { 10 }{ 100 } \)x 900 + 900
= 90+ 900 = Rs. 990
He also sold another electric iron at 5% loss.
Cost price of another electric iron = Rs.1200
So, selling price of the electric iron = 1200\(\frac { 5 }{ 100 } \) x 1200
= 1200-60 = Rs.1140
Total amount paid by Avinash for purchasing electric irons = Rs. 900 + Rs.1200 = Rs.2100 Total received amount = Rs. 990 + Rs. 1140
= Rs. 2130 So, his profit = Rs.2130- Rs.2100 = Rs.30in transaction.
Hence, option (c) is correct.

Question. 18 A TV set was bought for t 26250 including 5% VAT. The original price of the TV set is
(a) Rs. 27562.50 (b) Rs. 25000 (c) Rs. 24937.50 (d) Rs. 26245
Solution. (c) Cost price of TV set = Rs. 26250.
VAT including = 5%
Original price = Cost price of article including VAT = 26250 \(\frac { 5 }{ 100 } \) x 26250
= 26250-\(\frac { 26250 }{ 20 } \)
= 26250-1312.5
So, original price of the TV set = Rs. 24937.5 Hence, option (c) is correct.

Question. 19 40% of [100 – 20% of 300] is equal to
(a) 20 (b) 16 (c) 140 (d) 64
Solution. (b) 40% of [100-20% of 300]
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Hence, option (b) is correct.

Question. 20 Radhika bought a car for Rs. 250000. Next year, its price decreased by 10% and further next year, it decreased by 12%. In the two years, overall decrease per cent in the price of the car is
(a) 3.2% (b) 22% (c) 20.8% (d) 8%
Solution. (c) Radhika bought a car for Rs. 250000.
Cost price of a car = Rs.250000
Its price decreased next year for 10%.
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Hence, option (c) is correct.

Fill in the Blanks
In questions 21 to 45, fill in the blanks to make the statements true.
Question. 21 ……………. is a reduction on the marked price of the article.
Solution.  Discount is a reduction on the marked price of the article.

Question. 22 Increase of a number from 150 to 162 is equal to increase of ………………..per cent.
Solution. Initial number = 150
Final number = 162
Increased number = 162 -150 = 12
Per cent of increased number = \(\frac { 12 }{ 150 } \) x 100 =\(\frac { 120 }{ 15 } \) = 8%

Question. 23 15% increase in price of an article, which is Rs. 1620, is the increase of ?
Solution. Let the price of the article be Rs. x.
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Question. 24 Discount =…………….
Solution. Discount = MP – SP
Here, MP = Marked price, and SP = Selling price

Question. 25 Discount = Discount % of ……………
Solution. Discount = Discount % of marked price
[ discount is a reduction given on marked price]

Question. 26 ………………….is charged on the sale of an item by the government and is added to the bill amount.
Solution.  Sales tax is charged on the sale of an item by the government and is added to the bill amount.
Sales tax = Tax % of bill amount

Question. 27 Amount when interest is compounded annually, is given by the formula……………….
Solution.  Amount when interest is compounded annually, is given by the formula
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where, P = principal, R = rate per annum and T = time

Question. 28 Sales tax = Tax% of……………….
Solution. Sales tax=Tax % of bill amount

Question. 29 The time period after which the interest is added each time to form a new principal, is called the ……………
Solution. The time period after which the interest is added each time to form a new principal, is called the conversion period.

Question. 30 ……………… expenses are the additional expenses incurred by a buyer for an item over and above its cost of purchase.
Solution. Overhead expenses are the additional expenses incurred by a buyer for an item over and above its cost of purchase.

Question. 31 The discount on an item for sale is calculated on the ……………..
Solution. The discount on an item for sale is calculated on the marked price.

Question. 32 When principal P is compounded semi-annually at r% per annum for t years, then amount = ……………..
Solution. When principal P is compounded semi-annually at r% per annum for t years.
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Question. 33 Percentages are to fractions with ………………. equal to 100.
Solution.  Percentages are equal to fractions with denominator equal to 100.
e.g. 8% means \(\frac { 8 }{ 100 } \)

Question. 34 The marked price of an article when it is sold for ? 880 after a discount of 12%, is ……………..
Solution. Selling price of an article = Rs.880 Discount % = 12%
We know that, discount is calculated oh marked price. Let the marked price be Rs. x.
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Question. 35 The compound interest on Rs. 8000 for one year at 16% per annum compounded half-yearly is …………… , given that \({ 1.08 }^{ 2 }\) = 1.1664.
Solution. Given, principal(P) = Rs.8000
Time period (7) = 1 yr
Rate (ft) = 16% per annum compounded half-yearly

Question. 36 In the first year on an investment of Rs. 600000, the loss is 5% and in the second year, the gain is 10%, the net result is ……………….
Solution. Investment amount = 7600000
In 1st year, the loss in 1st year = 5%.
So, investment in 1st year = 600000 – \(\frac { 5 }{ 100 } \) x 600000= 600000 – 30000 = 7 570000
In llnd year, the gain is 10%.
So, net investment = 570000 +\(\frac { 10 }{ 100 } \) x 570000= 570000 + 57000 = 7627000

Question. 37 If amount on the principal of Rs. 6000 is written as 6000 \({ \left[ 1+\frac { 5 }{ 100 } \right] }^{ 3 }\)and compound interest payable half-yearly, then rate of interest per annum is…………….. and……………… time (in years) is
Solution. If amount on the principal of 7 6000 is written as 6000\({ \left[ 1+\frac { 5 }{ 100 } \right] }^{ 3 }\) of and compound interest
payable half-yearly, then rate of interest per annum is 10% and time (in years) is 1\(\frac { 1 }{ 2 } \) yr.

Question. 38 By selling an article for Rs. 112000, a girl gains 40%. The cost price of the article was ……………..
Solution. Selling price of an article = 7 112000
Gain% = 40% .
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Question. 39 The loss per cent on selling 140 geometry boxes at the loss of SP of 10 geometry boxes is equal to ………………..
Solution. Let the selling price of 1 geometry box be Rs. 1.
So, the selling price for 140 geometry boxes = Rs.1 x 140 = Rs.140
Similarly, selling price of 10 geometry boxes = Rs. 1 x 10 = Rs. 10 v
Loss = Selling price of 10 geometry boxes = Rs.10
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Question. 40 The cost price of 10 tables is equal to the sale price of 5 tables. The profit per cent in this transaction is ……………..
Solution. Let the cost price of 1 table be Rs. 1.
The cost price of 10 tables = Sale price of 5 tables Profit = Cost price of 5 tables = Rs. 5
Profit percentage =\(\frac { profit }{ CP } \) x 100 = \(\frac { 5 }{ 5 } \)x 100 = 100%

Question. 41 Abida bought 100 pens at the rate of Rs. 3.50 per pen and pays a sales tax of 4%. The total amount paid by Abida is .
Solution. Number of pens bought by Abida = 100 Rate of per pen = Rs.3.50 So, cost of 100 pens = 100 x 3.50 = 1350 Abida also paid 4% sales tax on Rs. 350.
So, the total amount paid by Abida = 350x \(\frac { 4 }{ 100 } \) + 350= 350 x \(\frac { 1 }{ 25 } \) + 350= 14+ 350
= Rs. 364 .

Question. 42 The cost of a tape recorder is Rs. 10800 inclusive of sales tax charged at 8%. The price of the tape recorder before sales tax was charged, is ……………….
Solution. The cost of tape recorder, inclusive of 8% sales tax = Rs.10800 Let the price of the tape recorder before sales tax be Rs. x.
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Question. 43 2500 is greater than 500 by …………..%.
Solution. Difference between 2500 and 500 = 2500 – 500 = 2000
Hence, \(\frac { 2000 }{ 500 } \) x 100 = \(\frac { 2000 }{ 5 } \) = 400%

Question. 44 Four times a number is a …………….% increase in the number.
Solution. Let x be the number.
So, four times of x is Ax.
Hence, Ax is greater than x by 4x – x = 3x
Percentage increase in x = \(\frac { 3x }{ x } \) x 100 = 300%

Question. 45 5% sales tax is charged on an article marked X 200 after allowing a discount of 5%, then the amount payable is …………….
Solution. The marked price of the article = 1200 Discount = 5%
Selling price of the article = 200 – \(\frac { 5 }{ 100 } \) x 200
=200 -10 = Rs.190
Selling price including 5% sales tax = 190 + \(\frac { 5 }{ 100 } \) x 190
= 190+ 9.5 = Rs.199.5
Payable amount = Rs. 199.50

True/False
Inquestions 46 to 65, state whether the statements are True or False.
Question. 46.Tp calculate the growth of a bacteria if the rate of growth is known, the formula for calculatiorfof amount in compound interest can be used.
Solution. True
For calculating the growth of a bacteria4f the rate of growth is known, then we can use the formula for calculation of amount in compound interest.where, A = growth after nyears, P = initial number of bacteria and R = rate of growth

Question. 47 Additional expenses made after buying an article are included in the cost price and are known as Value Added Tax.
Solution. False
In the selling price (known as MRP) include the tax known as VAT (Value Added Tax).
Hence, VAT is always included in selling price.

Question. 48 Discount is a reduction given on cost price of an article.
Solution. False
Discount is a reduction given on marked price not on cost price.

Question. 49 Compound interest is the interest calculated on the previous year’s amount.
Solution. True
v Compound interest, Cl = A – P
where,
\({ A=P\left[ 1+\frac { R }{ 100 } \right] }^{ n }\)
Here, P = Principal on previous year’s amount and A = Present year’s amount R = Rate of interest and n = Time

Question. 50 CP = MP – Discount
Solution. False
The relation between marked price and discount is given by Selling price = Marked price – Discount

Question. 51 A man purchased a bicycle for Rs. 1040 and sold it for Rs. 800. His loss per cent is 30%.
Solution. False
Cost pride of the bicycle = Rs. 1040 Selling price of the bicycle =Rs. 800
Loss = Cost price – Selling price = Rs.1040 -Rs.800 = Rs.240
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Question. 52 Three times a number is 200% increase in the number, then one-third of the same number is 200% decrease in the number.
Solution. False
Let x be the number.
So, three times of x = 3x
Difference between 3x and x=3x-x=2x
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Question. 53 Simple interest on a given amount is always less than or equal to the compound interest on the same amount for the same time period and at the same rate of interest per annum.
Solution. False
For 1 yr, the simple interest and compound interest for same amount on same rate of interest are equal.
But for 2 yr, the simple interest is less than the compound interest for same amount on same rate of interest.

Question. 54 The cost of a sewing machine is Rs. 7000. Its value depreciates at 8% per annum. Then, the value of the machine after 2 yr is Rs. 5924.80.
Solution. True
Principal = Rs.7000
Rate of depreciation = 3% per annum Time period = 2 yr
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Question. 55 If the discount of Rs. y is available on the marked price of Rs. x, then the discount per cent is\(\frac { x }{ y }\) x 100%,
Solution. False
Marked price =Rs.x
Discount amount =Rs.y
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Question. 56 Number of students appearing for class X CBSE examination increases from 91422 in 1999-2000 to 116054 in 2008-09. Increase in the number of students appeared is approximately 27%.
Solution. True
Number of students increase from 116054 in 2008-09 to 91422 in 1999-2000
= 116054 – 91422 = 24632
Percentage of increase in number of students
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Question. 57.Selling price of 9 articles is equals to the cost price of 15 articles .In this transaction the profit of 66\(\frac { 2 }{ 3 }\)%
Solution. True

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Question. 58The compound interest on a sum of Rs. P for T years at R% per annum compounded annually is given by the formula,\(P\left[ 1+\frac { R }{ 100 } \right] \)
Solution. False
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Question. 59 In case of gain, SP =\(\frac { (100+gain%)\times CP }{ 100 } \)
Solution. True
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Question. 60 In case of loss, CP =\(\frac { 100\times SP }{ 100+Loss% } \)
Solution. False
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Question. 61 The value of a car, bought for Rs. 440000 depreciates each year by 10% of its value at the beginning of that year. So, its value becomes Rs. 308000 after three years.
Solution. False
The value of a car i.e. principal = Rs.440000 Rate of depreciation (R%) = 10% per annum Time period (T) = 3 yr
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Question. 62 The cost of a book marked at Rs. 190 after paying a sales tax of 2% is Rs. 192.
Solution. False
Marked price of a book = Rs.190 .
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Question. 63 The buying price of 5 kg of flour with the rate Rs. 20 per kg, when 5% sates tax is added on the purchase, is Rs. 21.
Solution. True
Total flour bought = 5 kg
Rate of one kg flour = Rs.20
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Question. 64 The original price of a shampoo bottle bought for Rs. 324, if 8% VAT is included in the price, is Rs. 300.
Solution. False
The original price of a shampoo bottle = Rs.300
Cost price of shampoo bottle after 8% VAT
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Question. 65 Sales tax is always calculated on the cost price of an item and is added to the value of the bill.
Solution. False
Sales tax is always calculated on the selling price of an item and is added to the value of the bill.

Question. 66 In a factory, women are 35% of all the workers, the rest of the workers being men. The number of men exceeds that of women by 252. Find the total number of workers in the factory.
Solution. Percentage of women in factory = 35%
Percentage of men in factory = 100 – 35 = 65%
Let the number of persons in the factory be x.
According to the question,
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Question. 67 Three bags contain 64.2 kg of sugar. The second bag contains \(\frac { 4 }{ 5 }\) of the contents of the first and the third contains 45 \(\frac { 1 }{ 2 }\) % of what there is in the second bag. How much sugar is there in each bag?
Solution. The total weight of sugar in three bags = 64.2 kg Let the first bag contains x kg sugar.
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Question. 68 Find the SP, if
(a) MP = Rs. 5450 and discount = 5%
(b) MP = Rs.1300 and discount = 15%
Solution. (a) Marked price = 7 5450 Discount % = 5%
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Question. 69 Find the MP, if
(a) SP = Rs. 495 and discount = 1%
(b) SP = Rs. 9250 and discount = 7\(\frac { 1 }{ 2 }\) %
Solution. (a) Selling price (SP) = 7495 Discount % = 1%
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Question. 70 Find discount in percent when
(a) MP = Rs.625 and SP = Rs.562.50
(b) MP = Rs.900 and SP = Rs.873
Solution.  (a) Marked price (MP) = Rs.625 Selling price (SP) = Rs. 562.50
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Question. 71 The marked price of an article is Rs. 500. The shopkeeper gives a discount of 5% and still makes a profit of 25%. Find the cost price of the article.
Solution. Given, marked price of an article = Rs.500 Discount % = 5%
But it makes a profit of 25%.
Let the cost price of the article be Rs. x.
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Question. 72 In 2007-08, the number of students appeared for Class X examination was 105332 and in 2008-09 the number was 116054. If 88151 students pass the examination in 2007-08 and 103804 students in 2008-09. What is the increase or decrease in pass percentage in class X result?
Solution.  Number of students appeared in 2007-08 = 105332 Number of students appeared in 2008-09 = 116054 Number of students passed in 2007-08 = 88151 Number of students passed in 2008-09 = 103804
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Question. 73 A watch worth Rs. 5400 x is offered for sale at Rs. 4500. What per cent discount is offered during the sale?
Solution. Marked price of a watch = Rs.5400
Selling price = Rs.4500
Discount = Marked price – Selling price = Rs.5400 – Rs.4500 = Rs.900
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Question. 74 In the year 2001, tbe number of malaria patients admitted in the hospitals of a state was 4375. Every year this number decreases by 8%. Find the number of-patients in 2003.
Solution. The number of malaria patients admitted in a hospital in 2001 = 4375 Rate of decrement of malaria patients = 8%
Time period = 2 yr i.e.2003-2001=2 yr
Let the number of patients in 2003 be A.
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Question. 75 Jyotsana bought a product for Rs. 3155 including 4.5% sales tax. Find the price before tax was added.
Solution. A product bought by Jyotsana for Rs. 3155 including 4,5% sales tax.
Let the price of the product before sales tax be Rs. x.
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Question. 76 An average Urban Indian uses about 150 L of water everyday.
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(a) What per cent of water is used for bathing and sanitation together per day?
(b) How much less per cent of water is used for cooking in comparison to that used for bathing?
(c) What per cent of water- is used fdr drinking, cooking and gardening together?
Solution. (a) On the basis of given details, water used for bathing per day = 20 L
Water used for sanitation = 40 L
Total water used per day = 150 L
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Question. 77 In 1975, the consumption of water for human use was about 3850 cu km/yr. It increased to about 6000 cu km/yr in the year 2000.
Find the per cent increase in the consumption of water from 1975 to 2000. Also, find the annual per cent increase in consumption
(assuming water consumption increases uniformly).
Solution. The consumption of water for human in 1975 = 3850 cu km/yr
The consumption of water for human in 2000 = 6000 cu km/yr
Increase in consumption of wgjer in 1975 to 2000 = 6000 – 3850 = 2150 cu km/yr
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Question.  78 Harshna gave her car for service at service station on 27-05-2009 and was charged as follows
(a)3.10 L engine oil @ Rs. 178.75 per litre and VAT @ 20%.
(b)Rs. 1105.12 for all other services and VAT @ 12.5%.
(c)Rs. 2095.80 as labour charges and service tax @ 10%.
(d)3% cess on service tax.
Find the bill amount.
Solution. (a) The total litres of engine oil used = 3.10 L
Rate of engine oil per litres =Rs. 178.75
The cost of engine oil = 3.10 x 17875= Rs. 554.125
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Question. 79 Given, the principal = Rs.40000, rate of interest = 8% per annum compound annually. Find
(a) Interest if period is one year.
(b) Principal for Ilnd year.
(c) Interest for Ilnd year.
(dj Amount if period is ttoo year.
Solution. Given, principal (P)= Rs.40000
Rate of interest (R) = 8% per annum
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Question. 80 In Delhi University, in the year 2009-10, 49000 seats were available for admission to various courses at graduation level. Out of these 28200 seats were for the students of General Category while 7400 seats were reserved for SC and 3700 seats for ST. Find the percentage of seats available for
(a) students of General Category.
(b) students of SC Category and ST Category taken together.
Solution. The total number of seats available for admission in 2009-10 = 49000
Seats reserved for General Category students = 28200
Seats reserved for SC Category students = 7400
Seats reserved for ST Category students = 3700
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Question. 81 Prachi bought medicines from a medical store as prescribed by her doctor for Rs 36.40 including 4% VAT. Find the price of before VAT was added.
Solution.
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Question. 82 Kritika ordered one pizza and one garlic bread from a pizza store and paid Rs 387 inclusive of taxes of Rs 43. Find the tax%.
Solution.
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Question. 83 Arunima bought household items whose marked price and discount % is as follows
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Find the total amount of the bill she has to pay.
Solution.
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Question. 84 Devangi’s phone subscription charges for the period 17-02-09 to 16-03-09 were as follows
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Find the final bill amount, if 3% education cess was also charged on service tax.
Solution.
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Question. 85 If principal = Rs 100000, rate of interest = 10% compounded half-yearly. Find.
(a) Interest for 6 months. (b) Amount after 6 months.
(c) Interest for next 6 months, (d) Amount after one year.
Solution.
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Question. 86 Babita bought 160 kg of mangoes at Rs 48 per kg. She sold 70% of the mangoes at Rs 70 per kg and the remaining mangoes at Rs 40 per kg. Find Babita’s gain or loss per cent on the whole dealing.
Solution.
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Question. 87 A shopkeeper was selling all his items at 25% discount. During the off season, he offered 30% discount over and above the existing discount. If Pragya bought a skirt which was marked for Rs 1200, how much did she pay for it?
Solution.
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Question. 88 Ayesha announced a festival discount of 25% on all the items in her mobile phone shop. Ramandeep bought a mobile phone for himself. He got a discount of ? 1960. What was the marked price of the mobile phone?
Solution.
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Question. 89 Find the difference between compound interest and simple interest on Rs 45000 at 12% per annum for 5 yr.
Solution.
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Question. 90 A new computer costs Rs 100000. The depredation of computers is very high as new models with better technological advantages are coming into the market. The depredation is as high as 50% every year. How much will the cost of computer be after two years?
Solution.
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Question. 91 The population of a town was decreasing every year due to migration, poverty and unemployment. The present population of the town is 631680. Last year the migration was 4% and the year before last, it was 6%. What was the population two years ago?
Solution.
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Question. 92 Lemons were bought at Rs 48 per dozen and sold at the rate of Rs 40 per 10. Find the gain or loss per cent.
Solution.
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Question. 93 If the price of petrol, diesel and LPG is slashed as follows
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Complete the above table.
Solution.
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Question. 94 What is the percentage increase or decrease in the number of seats won by A, B, C and D in the general elections of 2009 as compared to the results of 2004?
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Question. 95 How much more per cent seats were won by X as compared to Y in assembly election in the state based on the data given below?
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Question. 96 Ashima sold two coolers for ? 3990 each. On selling one cooler she gained 5% and on selling the other she suffered a loss of 5%. Find her overall gain or loss % in whole transaction.
Solution.
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Question. 97 A lady buys some pencils for Rs 3 and an equal number for Rs 6. She sells them for Rs 7. Find her gain or loss %.
Solution.
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Question. 98 On selling a chair of Rs 736, a shopkeeper suffers a loss of 8%. At what price should he sell it, so as to gain 8%?
Solution.
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Question. 99 A dining table is purchased for Rs 3200 and sold at a gain of 6%. If a customer pays sales tax at the rate of 5%. How much does the customer pay in all for the table?
Solution.
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Question. 100 Achal bought a second hand car for Rs 225000 and spend Rs 25000 for repairing. If she sold.it for Rs 325000, what is his profit per cent?
Solution.
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Question. 101 A lady bought an air-conditioner for Rs 15200 and spent Rs 300 and Rs 500 on its transportation and repair, respectively. At what price should she sell it to make a gain of 15%?
Solution.
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Question. 102 What price should a shopkeeper mark on a article that costs him Rs 600 to gain 20%, after allowing a discount of 10%?
Solution.
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Question. 103 Brinda purchased 18 coats at the rate of Rs 1500 each and sold them at a profit of 6%. If customer is to pay sales tax at the rate of 4%, how much will one coat cost to the customer and what will be the total profit earned by Brinda after selling all coats?
Solution.
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Question. 104 Film borrowed Rs 1024000 from a bank for one year. If the bank charges interest of 5% per annum, compounded half-yearly, what amount will he have to pay after the given time period. Also, find the interest paid by him.
Solution.
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Question. 105 The following items are purchased from showroom T-Shirt worth Rs 1200 Jeans worth Rs 1000 2 skirts worth Rs 1350 each.What will these items cost to Shikha if the sales tax is 7%?
Solution.
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Question. 106 The food labels given below information about 2 types of soup cream of tomato and sweet corn. Use these labels to answer the given questions, (all the servings are based on a 2000 calories diet.)
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(a) Which can be measured more accurately the total amount of fat it cream of tomato soup or the total amount of fat in sweet corn soup? Explain.
(b) On serving of cream of tomato soup contains 29% of the recommended daily value of sodium for a 2000 calories diet. What is the recommended daily value of sodium in milligrams? Express the answer up to 2 decimal places.
(c) Find the increase per cent of sugar consumed, if cream of tomato soup is chosen over sweet corn soup.
(d) Calculate ratio of calories from fat in sweet corn soup to the calories from fat in cream of tomato soup.
Solution.
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Question. 107 Music CD originally priced at Rs 120 is on sale for 25% off. What is the SP? Sonia and Rahul have different ways of calculating the sale price for the items they bought.
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As you work on the next problem, try both of these methods to see which your refer.
Solution.
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Question. 108 Store A and store B both charge Rs 750 for a video game. This week the video game is on sale Rs 600 at store B and for 25% off at store A. At which store is the game less expensive?
Solution.
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Question. 109 At a toy shop price of all the toys is reduced to 66% of the original price.
(a) What is the sale price of a toy that originally costs Rs 90?
(b) How much money would you save on a toy costing Rs 90?
Solution.
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Question. 110 A store is having a 25% discount sale. Sheela has a Rs 50 gift voucher and wants to use it to buy a board game marked for Rs 320. She is not sure how to calculate the concession she will get. The sales clerk has suggested two ways to calculate the amount payable.
Method 1 Subtract Rs 50 from the price and take 25% off the resulting price.
Method 2 Take 25% off the original price and then subtract Rs 50.
(a) Do you think both the methods will give the same result? If not, predict which method will be beneficial for her.
(b) For each method, calculate the amount Sheela would have to pay. Show your work.
(c) Which method do you think stores actually use? Why?
Solution.
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Question. 111 Living on your own Sanjay is looking for one bedroom appartment on rent. At Neelgiri appartments, rent for the first two months is 20% off. The one bedroom rate at Neelgiri is Rs 6000 per month. At Savana appartments, the first month is 50% off. The one bedroom rate at Savana appartments is Rs 7000 per month. Which appartment will be cheaper for the first two months? By how much?
Solution.
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Question. 112 For an amount, explain why, a 20% increase followed by a 20% decrease is less than the original amount.
Solution.
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Question. 113 Sunscreens block harmful ultraviolet (UV) rays produced by the sun. Each sunscreen has a Sun Protection Factor (SPF) that tells you how many minutes you can stay in the sun before you receive one minute of burning UV rays. e.g. If you apply sunscreen with SPF 15, you get one minute of UV rays for every 15 minutes you stay in the sun.
(i) A sunscreen with SPF 15 allows only \(\frac { 1 }{ 15 } \) of the sun’s UV rays. What per cent of UV rays does the sunscreen abort?
(ii) Suppose, a sunscreen allows 25% of the sun’s UV rays.
(a) What fraction of UV rays does this sunscreen block? Give your answer in lowest terms.
(b) Use your answer from part (a) calculate this sun screen’s SPF. Explain how you found your answer?
(iii) A label on a sunscreen with SPF 30 claims that the sunscreen blocks , about 97% of harmful UV rays. Assuming the SPF factor is accurate,is this claim true. Explain.
Solution.
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Question. 114 A real estate agent receives Rs 50000 as commission, which is 4% of the selling price. At what price does the agent sell the property?
Solution.
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Question. 115 With the decrease in prices of tea by 15%, Tonu, the chaiwallah, was able to buy 2 kg jnore of tea with the same Rs 45 that he spent each month on buying tea leaves for his chai shop. What was the reduced price of tea? What was the original price of tea?
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Question. 116 Below is the report card of Vidit Atrey. Vidit’s teacher left the last column blank. Vidit is not able to make out, in which subject he performed better and in which he needs improvement. Complete the table to help Vidit know his comparative performance.Assessment report for- 2009-2010
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Question. 117 Sita’s practicing basket ball. She has managed to score 32 baskets in 35 attempts. What is her success rate in percentage?
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Question. 118 During school hours, Neha finished 73% of her homework and Minakshi completed \(\frac { 5 }{ 8 } \) of her, homework. Who must finish a greater per cent of 8 homework?
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Question. 119 Rain forests are home to 90000 of the 250000 identified plant species in the world. What per cent of the world’s identified plant species are found in rain forests?
Solution.
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Question. 120 Madhu’s room measures 6m x 3m. Her carpet covers 8 \({ m }^{ 2 }\). What per t cent of floor is covered by the carpet?
Solution.
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Question. 121 The human body is made up mostly of water. In fact about 67% of a person total body weight is water. If Jyoti weights 56 kg, how much of her weight is water?
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Question. 122 The per cent of pure gold in 14 carat gold is about 58.3%. A 14 carat gold ring weights 7.6 grams. How many grams of pure gold are in the ring?
Solution.
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Question. 123 A student used the proportion \({ n }^{ 100 }\)=\({ 5 }^{ 32 }\) to find 5% of 32. What did the student do wrong?
Solution.
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Question. 124 The table shows the cost of sunscreen of two brands with and without sales tax. Which brand has a greater sales tax rate? Give the sales tax rate of each brand?
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The post NCERT Exemplar Problems Class 8 Mathematics Comparing Quantities appeared first on Learn CBSE.

CBSE Sample Papers for Class 12 Economics Outside Delhi – 2008

Time allowed : 3                                                                                                                                 hours Maximum marks 100

GENERAL INSTRUCTIONS
(i) All questions in both the sections are compulsory.
(ii) Marks for questions are indicated against each.
(iii) Questions No. 1-5 and 17-21 are very short-answer questions carrying 1 nic-k each. They are required to be answered in one sentence each.
(iv) Questions No. 6-10 and 22-26 are? short-answer questions carrying 3 marks each. Answers to them should normally not exceed 60 words each.
(v) Questions No. 11-13 and 27-29 are also short-answer questions carrying 4 marks each. Answers to them should normally not exceed 70 words each.
(vi) Questions No. 14-16 and 30-32 are long-ansxoer questions carrying 6 marks each. Answers to them should normally not exceed 100 words each.
(vii) Answers should be brief and to the point and the above word limit should be adhered to as far as possible.

SET I

SECTION A

Question.l. Define ‘Marginal Rate of Transformation’.
Answer. Marginal Rate of Transformation is the rate at which one more unit of any good X is substituted for good Y. Symbolically,
MRT=\(\frac { \Delta Y }{ \Delta X }\)

Question.2. What is a demand schedule?
Answer. It is a two-column table which indicates various quantities demanded corresponding to various market prices.

Question.3. Define ‘production function’.
Answer. Production function explains the relationship between factor inputs and output under given j technology.

Question.4. What is ‘market supply’.
Answer.It is the total supply of a product (commodity) of all the producing firms at a given price at a given time.

Question.5. Define ‘equilibrium price’.
Answer. The price, where quantity demanded and quantity supplied are equal, is equilibrium price.
Any price other than this will lead to a situation of either excess demand or excess supply.

Question.6. Explain the central problem of ‘choice of technique’.
Answer. A number of techniques are available for producing a commodity, such as more of labour and less of capital or less of labour and more of capital. Therefore, a firm has to decide as } to which technique should be used for producing a commodity. This choice is made because
of the difference in the availability of resources. The technique, which is the cheapest, should be used. If labour is abundant and cheap, labour intensive technology would lead to cost effective production.
In case labour is scarce and costly, capital intensive technology would be used.

Question.7. Price elasticity of demand of a good is (-) 1. At a given price the consumer buys 60 units of the good. How many units will the consumer buy if the price falls by 10 per cent?
% change in quantity demanded
Answer.
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Question.8. Given the market price of a good. How does a consumer decide as to how many units of that good to buy? Explain.
Answer. This is a question which signifies as to how consumers equilibrium is established in the case of a single commodity. It cannot be decided at the point of equality of price and marginal utility of the commodity because these two variables are incomparable. Therefore, the equilibrium will be established at a point where price of the commodity is equal to its marginal utility in money form i.e., \({ MU }_{ x }\) = \( MU }_{ m }\)

Question.9. What is the likely effect on the supply of a good if the prices of the inputs used in production of that good fall? Explain.
Answer. Fall in the prices of inputs decreases the cost of 8 production as a result of which supply will increase. In such a case, as shown in Diagram 1, a shift towards right takes place in the supply curve.
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Question.10. Explain what happens to the profits in the long run if the firms are free to enter the industry.
Answer. In the long run the firm will earruoQly normal profit (AR = AC) when new firms are free to enter the industry. This is so because if existing firms are earning abnormal profit (AR > AC) entry of new firms will increase the supply leading to decline in price. As a result of this excess of AR over AC will disappear and firms will get only normal profits.
(or)
Explain what happens to losses in the long run if the firms are free to leave the industry.
Answer. In the long run, if the firms are free to leave the industry, the existing firms will not sustain losses and earn only normal profits. This is so because in the case of losses few firms will leave the industry leading to decline in supply and increase in price. Ultimately, it will create a situation of normal profit.

Question.11. Explain producer’s equilibrium using a schedule. Use total cost and total revenue approach.
Answer. See Q. 11, 2008 (I Delhi)
Or
Distinguish between (i) fixed cost and variable cost giving examples and (ii) average cost and marginal cost giving an example.
Answer. (i) Fixed Cost: It is the cost which remains fixed and does not change with the change in , the level of output, such as rent of the building.
Variable Cost: It is the cost which varies directly with the changes in the level of output, such as cost of raw material. This cost will be zero when level of output is zero.
(ii) Average Cost: It is the cost which is obtained by dividing the total cost (TC) by the number of units produced. In shorty
\(AC=\frac { TC }{ Number\quad of\quad units\quad produced } \)
Marginal Cost (MC): The change in total cost that takes place by producing an additional unit is marginal cost. In short, MC = TC(n units) – TC(n-1 units).

Question.12. Draw supply curves with price elasticity of supply throughout equal to (i) zero, (ii) one, (iii) infinity and (iv) less than one.
Answer.
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For Blind Candidate only in lieu of

Question. No. 12 Distinguish between (i) elastic and inelastic supply and (ii) perfectly elastic and perfectly inelastic supply.
Answer. (i) When proportionate change in supply is more than the proportionate change in price, the supply is elastic or >1.
On the other hand, when proportionate change in supply is less than the proportionate .change in price, the supply is inelastic or <1.
(ii) When supply changes to any extent without changes in price, the supply is perfectly elastic. On tire other hand, if supply does not change and remains fixed when price changes, supply is said to be perfectly inelastic, i.e., es = 0.

Question.13. Complete the following table:
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Answer.
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Question.14. Explain the effect of the following on demand for a good:
(i) Rise in income
(ii) Rise in prices of related goods
Answer. (i) Effect of rise in income on the demand for a good. Due to the direct relationship between income and demand, the income demand curve rises upwards to the right. However, this is not true in the case of ail the commodities. When income rises the demand for normal and superior goods rises and the demand for inferior goods declines. Thus, as shown in Diagram 3, the income demand curve of normal goods rises upwards to the right and demand curve for inferior goods slopes downwards to the right .
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(ii) Effect of rise in the prices of related goods. Related goods can be of two types (i) substitute goods and (ii) complementary goods. Substitute goods are those which can be used in place of one another such as tea and coffee. Complementary goods are those which cannot be used without one another, such as car and petrol.
When the price of a a commodity changes, it ‘ affects the demand far its substitute goods in the opposite manner. For example, if the price of tea increases, its demand will fall but the demand for coffee will increase because’it becomes cheaper in comparison to tea. Thus, as shown in Diagram 4, a shift in demand curve for coffee will lake place towards right when price of tea rises.
If the. price of a good rises (say pen), its demand falls. Thus rise in the price of pen will affect the demand for ink in the same maimer because it is a complemehfary good. Thus, when the price of a good increases, its demand falls and the demand of its complementary good also falls This iS being shown in Diagram 5.

Question.15. Explain, with the help of numerical examples, the effect on total output of a good when all the inputs used in production of that good are increased simultaneously and in the same proportion.
Answer. (Out of syllabus, for 2012 examination and orifflards)

Question.16. Given market equilibrium of a good, what are the effects of simultaneous increase in both demand and supply of that good on its equilibrium price and quantity.
Answer. Market equilibrium of a good is established at a point where quantity demanded is equal to quantity supplied. However, if changes take place in demand and supply,’equilibrium price and quantity are affected in accordance with changes in demand and supply* If demand and supply both increase, their effect on price and quantity can be examined under three situations as given below:
(i) When increase in demand is more than the increase in supply: As shown in diagram 6, price and quantity both will increase. Price will increase from OP to OP, and quantity will increase from OQ to OQ1.
(ii) When increase in demand and supply is equal: As shown in diagram 7, price will in Diagram 8, price will fall and quantity will increase. Price will decline from OP to OP, and quantity will increase from OQ to OQ.
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(iii) When increase in demand is less than the
increase in supply: In this case, as price will in Diagram 8, price will fall and quantity will increase. Price will decline from OP to OP, and quantity will increase from OQ to OQ.
(or)
Explain the implications of the following:
(i) The feature ‘differentiated products’ under monopolistic competition.
(ii) The feature Targe number of sellers’ undeir perfect competition.
Answer. (i) Under monopolistic competition, products are differentiated on the basis of their size, packing, colour, smell, brand name, etc., such as different kinds of tooth pastes. These are artificial differences created with a view to make a consumer habituated by using a particular brand of a commodity. With the result, even when the price of the brand commodity that the customer is used to, goes up, he does not reduce his demand for that. As such, because of product differentiation the firms have some price control. (ii) Under perfect competition, the number of buyers and sellers of the commodity is very large, it is so large that no individual buyer or seller can influence the price of commodity. The price is fixed by the supply and demand of the whole industry and the, s^, .determined price is accepted by all the firms. As a result of this aspect of perfect competition, a firm gets only normal profit in the long run. In the event of price (AR) being higher than cost (AC), few firms will join the cornpetition, On tiie other hand, in the event of loss, few firms will leave the competition. In both the cases, profits will be normal.

SECTIONS
Question.17. Define ‘aggregate supply’.
Answer. It is the total value of goods and services produced in an economy at a given time.

Question.18. Give meaning of deficient demand.
Answer. It signifies deficiency in aggregate demand in comparison to aggregate supply at the full employment level.

Question.19. What is a commercial bank?
Answer. It is an institution which deals in money and credit.

Question.20. Define government budget.
Answer. A government budget is a statement of estimated receipts and expenditure prepared annually for a fiscal year.

Question.21. What is fixed exchange rate system?
Answer. It is a system under which exchange is officially fixed and declared. This means exchange rate is fixed and does not vary with the changes in the demand for and supply of foreign currency. Only the government has the power to change it.

Question.22. Calculate Net Value Added at factor cost from the following data:
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Answer. Net Value Added at FC
= Sales + Change in stock + Exports – Import of raw. material + Subsidy – Intermediate cost – Depreciation
= (iv) + (vi) – (v) – (vii) + (iii) – (ii) – (i)
= 140 + (-10) + 7-3 + 5 – 90 – 20
= 152 – 123 = Rs. 29 lakhs.

Question.23. When exchange rate of foreign currency falls, its demand rises. Explain, how.
Answer. There is an inverse relationship between the foreign exchange rate and the .demand for foreign exchange. This means higher the foreign exchange rate, lower is the demand for foreign exchange and vice-versa. If the foreign exchange rate falls, this means that in
exchange of the given amount of horde currency more foreign exchange is available. If foreign exchange becomes cheaper, its demand will increase. For example, if external value of dollar in Indian rupee falls from Rs. 50 to Rs. 40, more goods can be obtained with the given amount of home currency, therefore demand for foreign exchange will increase.

Question.24. Distinguish between balance of trade and balance on current account.
Answer. Balance of trade relates to the payments made and received on account of import and export of goods only, i.e., visible items. However, balance on current account, besides including balance of trade, also includes payments relating to invisible items Mid hrdlateral transfers. Thus, balance on current account is a broader term in comparison to balance of trade.

Question.25. Explain the’medium of exchange’function of money.
Answer. An important function of money is that it functions as a medium of exchange. It facilitates transactions of goods and services. Producers sell their goods to the Wholesalers in exchange of money. Wholesalers sell the same goods to the consumers in exchange of money. In the same way, all sections of society sell their services in exchange of money and with that money buy goods and services which they need. Money, working as medium of exchange, has eliminated inconvenience which was faced in barter transactions. However, bank money can operate as medium of exchange’only when it is generally accepted in that role. Bank money can be treated as money simply on the basis of its general acceptability for it is highly useful.
Or
Explain the evolution of money.
Answer. (Out of syllabus, for 2011 examination and onwards)

Question.26. Give meaning of capital expenditure and revenue expenditure in a government budget.
Answer. Capital expenditure. An expenditure which results in the creation of assets or reduction in liabilities is treated as capital expenditure, such as expenditure incurred on construction of buildings, roads, bridges, etc.
Revenue expenditure. An expenditure which does not result in creation of assets or reduction of liabilities, is called revenue expenditure such as payments of salaries, pensions, etc.

Question.27. In an economy an increase in investment leads to increase in National Income which is three times the increase in investment. Calculate marginal propensity to consume.
Answer.
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