PERCENTAGES. cent implies hundred and hence percent implies for every hundred.

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1 PERCENTAGES PROFIT AND LOSS PERCENTAGES cent implies hundred and hence percent implies for every hundred. How to convert any fraction to percentage? Consider one fraction suppose 6/13 and we have to represent it in percentage. This can be done as follows: 6 13 = (6 100)/13 = = = 46.15% How to convert a percentage into a fraction? Suppose we have to convert 30% to fraction then we can do it as follows: 30% = = 0.3 Hence, any percentage can be expressed as a decimal fraction by dividing the percentage figure by 100 and conversely, any decimal fraction can be converted to percentage by multiplying it by 100. Percentage increase or decrease of a quantity is the ratio expressed in percentage of the actual increase or decrease of the quantity to the original amount of quantity. Thus, Percentage increase = Percentage decrease = AAAAAAAAAAAA iiiiiiiiiiiiiiii OOOOOOOOOOOOOOOO qqqqqqqqqqqqqqqq 100 AAAAAAAAAAAA ddddcccccccccccc OOOOOOOOOOOOOOOO qqqqqqqqqqqqqqqq 100 For example, if the price of an item is increased from Rs.100 to Rs.150 then the percentage increase can be calculated as follows: Actual increase in price = Rs. ( ) = Rs.50 Original price = Rs. 100 AAAAAAAAAAAA iiiiiiiiiiiiiiii Percentage increase = OOOOOOOOOOOOOOOO qqqqqqqqqqqqqqqq 100 = = 50% Whenever there is any percentage increase or decrease on a quantity, we can directly calculate the new value of the quantity instead of calculating the actual increase or decrease and then adding to or subtracting from the original quantity. For example, if the increase on a value of 200 is 25%, the new quantity is 1.25 x 200 (where 1.25=1+0.25, 0.25 being the decimal equivalent of 25%). Similarly, if there is a decrease of 20% on a quantity of 400, then the new quantity will be equal 400 x 0.8 (where 0.8 = 1 0.2, 0.2 being the decimal equivalent of 20%).

2 On the basis of percentage increase, we can write down how many times the old value gives the new value. For example, if the percentage increase is 100%, then we can conclude that the new value is 2 times the old value. If the percentage increase is 200%, the new value is 3 times the old value. in general, if the percentage increase is xx%, then the new value is xx + 1 times the old value. Conversely, if we know how many times the old value gives the new value, we can find out the percentage increase in the old value to get the new value. For example, if the value is 4 times the old value then the percentage increase in the old value to get the new value is 300%. If the new value is 1.12 times the old value then the percentage increase in the old value is 12%. in general, if the new value is y times the old value, then the percentage increase is (y 1) x 100. If there are successive increases of p%, q% and r% in three stages, the effective percentage increase is pp + qq + rr If one or more of p, q and r are decrease percentage figures and not increase percentage, then it will be taken as a negative figure and not as a positive figure. Similarly, if the resultant figure is negative, it means it is a net decrease. The same can be extended to any number of successive increase or decrease percentages. If the value of an item goes up/down by x%, the percentage reduction/increment to be now made to bring it back to the original level is 100xx % 100±xx If A is x% more/less than B, then B is 100xx % less/more than A. 100±xx If the price of an item goes up/down by x%, then the quantity consumed should be reduced/increased by 100xx % so that the total expenditure remains the same. 100±xx Percentage Points Percentage points is the difference of two percentage figures. PROFIT AND LOSS BASIC TERMS 1. Selling Price or Sale Price (S.P.) It is the price at which an item is sold. 2. Cost price (C.P.) It is the price at which an item is purchased. 3. Profit It is the extra money that is earned. 4. Loss When an item is sold below its cost price then loss is said to be incurred and the difference between the selling price and the cost price is known as loss. Formulae: Profit = Sale Price Cost Price = S.P. C.P. Percentage Profit = SS.PP. CC.PP. CC.PP. Loss = C.P. S.P. 100 = PPPPPPPPPPPP CC.PP

3 Percentage Loss = LLLLLLLL 100 CC.PP. It is customary to express Profit/Loss as percentage of Cost Price. However, in some problems it may specifically be given that profit/loss percentage has been calculated on the S.P. or the student may be asked to calculate the profit/loss percentage on the selling price. Unless such specific directions are given, the profit/loss percentage is always to be calculated on the cost price. When two articles are sold at the same price (i.e., their S.P. is the same) such that there is a profit of p% on one article and a loss of p% on the other (i.e., common profit or loss percentage), then, irrespective of what the S.P. actually is, the net result of the transaction is loss. This percentage loss is given by Loss Percentage = (CCCCCCCCCCCC pppppppppppp oooo llllllll )2 = pp Marked Price (M.P.) or List Price is the price that is indicated or marked on the product or it is the price which is given in the price list. This is the price at which the product is intended to be sold. However, there can be some discount given on this price and consequently, the actual S.P. of the product may be less than the M.P. S.P. = M.P. Discount Now, Discount percent = MM.PP. SS.PP. 100 = DDDDDDDDDDDDDDDD 100 MM.PP. MM.PP. Common Fractions with Decimal and Percent Equivalents It will be really helpful if you all memorize the below given table. Fraction Decimal Percent 1/ % 1/ % 1/ % 1/ % 1/ % 1/ % 1/ % 1/ % 1/ % 1/ %

4 1/ % 1/ % 1/ % 1/ % 1/ % 1/ % 2/ % 3/ % 2/ % 3/ % 4/ % 5/ % 3/ % 5/ % 7/ % 2/ % 4/ % 5/ % 7/ % 8/ %

5 PRACTICE EXERCISE 1. Alfred buys an old scooter for Rs 4700 and spends Rs 800 on its repairs. If he sells the scooter for Rs 5800, his gain percent is : a) b) c) 10 % d) 12 % 2. A shopkeeper purchased 70 kg of potatoes for Rs 420 and sold the whole lot at the rate of Rs 6.50 per kg. What will be his gain percent? a) b) c) d) 20 % 3. 28% of % of 280 =? a) 212 b) 232 c) 252 d) 272 e) None of these oranges are bought at the rate of Rs 350 and sold at the rate of Rs 48 per dozen. the percentage of profit or loss is : a) b) 15 % gain c) d) 15 % loss 5. a man buys a cycle for Rs 1400 and sells at a loss of 15 %. what is the selling price of the cycle? a) Rs 1090 b) Rs 1160 c) Rs 1190 d) Rs The ratio 5:4 expressed as a percent equals : a) 12.5% b) 40% c) 80% d) 125% can be expressed in terms of percentage as : a) 0.35% b) 3.5% c) 35% d) 350%

6 8. A fruit seller sells mangoes at a rate of Rs 9 per kg and thereby loses 20 %.at what price per kg should he sold them to gain a profit of 5 %? a) Rs b) Rs 12 c) Rs d) Rs Half of 1 percent written as a decimal is : a) b) 0.05 c) 0.02 d) A shopkeeper sells one transistor for Rs 840 at a gain of 20 % and another for Rs 960 at a loss of 4%. his total gain or loss percent is : a) b) c) d) None of these 11. What is 15 percent of Rs. 34? a) Rs.3.40 b) Rs.3.75 c) Rs.4.50 d) Rs The ratio between the sale price and the cost price of an article is 7 : 5. what is the ratio between the profit and the cost price of that article? a) 2: 7 b) 5: 2 c) 7: 2 d) Data inadequate e) None of these 13. A man gain 20 % by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be: a) 40 b) 100 c) 120 d) the profit earned by selling an article for Rs 832 is equal to the loss incurred when the same article is sold for Rs 448. what should be the sale price for making 50 % profit? a) Rs 920 b) Rs 960 c) Rs 1060 d) Rs 1200 e) None of these

7 15. the percentage profit earned by selling an article for Rs 1920 id equal to the percentage loss incurred by selling the same article for Rs at what price should the article be sold to make 25 % profit? a) Rs 2000 b) Rs 2200 c) Rs 2400 d) data inadequate e) None of these % of % of 210 -? = 118 a) 256 b) 258 c) 268 d) % of % of 860 =? a) 430 b) 516 c) 860 d) % of % of 480 =? a) 216 b) c) d) A man sold 18 cots for Rs 16800, gaining thereby the cost price of 3 cots. the cost price of the cot is : a) Rs 630 b) Rs 700 c) Rs 750 d) Rs If on selling 17 balls at Rs 720, there is a loss equal to the cost price of 5 balls. The cost price of the ball is : a) 45 b) 50 c) 55 d) If on selling 12 notebook, a seller make a profit equal to the selling price of 4 notebooks, what is his profit percentage? a) b) 25 c) 50 d) Data inadequate e) None of these 22. A man buys 2 dozen of banana at Rs 16 per dozen. after selling 18 bananas at the rate of 12 per dozen, the shopkeeper reduced the rate to Rs 4 per dozen. the

8 present loss is : a) 25.2 % b)32.4 % c) 36.5 % d) 37.5 % 23. A man bought apple at the rate of 8 for Rs 34 and sold them at the rate of 12 for Rs 57. How many apples should be sold to earn a net profit of Rs 45? 24. a) 90 b) 100 c) 135 d) 150 a) Rs 72 b) Rs 70 c) Rs d) Rs e) None of these % of ? = 35% of % of 850 a) 372 b) 842 c) 962 d) % of 264 is the same as : a) 10% of 44 b) 15% of 1056 c) 30% of 132 d) None of these is the percent of 0.1? a) b) c) 10 d) By selling 12 toffees for a rupee, a man loses 20 %. How many for a rupee he sell to get a gain of 20 %? a) 5 b) 8 c) 10 d) A trader mixes 26 kg of rice at Rs 20 per kg with 30 kg of rice of other variety at Rs 36 per kg and sells the mixture at Rs 30 per Kg. His profit percent is :

9 a) No profit, no loss b) 5 % c) 8 % d) 10 % e) None of these 30. Arun purchased 30 kg of wheat at the rate of Rs per kg and 20 kg of wheat at the rate of per kg. He mixes the two and sold the mixture. Approximately what price per kg should he sell the mixture to make 30 % profit? a) Rs b) Rs c) Rs d) Rs e) Rs A man buys an article for 10 % less than its value and sells it for 10 % more than its value. His gain or loss percent is : a) no profit, no loss b) 20 % profit c) < 20 % profit d) > 20 % profit 32. Peter bought an item at 20 % discount on its original price. He sold it with 40 % increase on the price he bought it. The new sale price is by what percent more than the original price? a) 7.5 b) 8 c) 10 d) 12 e) None of these 33. A shopkeeper sold an article offering a discount of 5 % and earned a profit of 23.5 %. What would have been the percentage of profit earned if no discount is offered? a) 24.5 b) 28.5 c) 30 d) Data inadequate e) None of these 34. A shopkeeper sold sarees at Rs 266 each after giving 5 % discount on labeled price. Had he not given the discount, he would have earned 12 % on the cost price. What is the cost price of each saree?

10 a) Rs 240 b) Rs 260 c) Rs 280 d) Data inadequate e) None of these 35. A shopkeeper sells 25 articles at Rs 45 per article after giving 10 % discount and earns 50 5 profit. If the discount is not given then the profit gained is : these a) 60% b) c) 66 % d) e) None of 36. A shopkeeper sold a T.V. set for Rs with a discount of 8 % and earned a profit of 19.6 %. What would have been the percentage of profit earned if no discount was offered? a) 24.8 % b) 25 % c) 26.4% d) Cannot be determined e) None of these 37. A shopkeeper sells a badminton racket, whose marked price is Rs 30, at a discount of 15 % and gives a shuttle cock costing Rs 1.50 free with each racket. Even then he makes a profit of 20 %. His cost price per racket is : a) Rs b) Rs 20 c) Rs 21 d) Rs What percent of Rs 2650 is Rs ? a) 60% b) 75% c) 80% d) 90% 39. What percent of a day is 3 hours? a) b) c) d) 40. A housewife saved Rs 2.50 in buying an item on sale. If she spent Rs 25 for the item, approximately how much percent she saved in transaction? a) 8% b) 9% c) 10% d) 11%

11 1. B 2. C 3. C 4. A 5. C 6. D 7. D 8. A 9. A 10. B 11. D 12. E 13. D 14. B 15. A 16. B Answers 17. C 18. B 19. D 20. D 21. C 22. D 23. A 24. A 25. C 26. B 27. C 28. B 29. B 30. D 31. D 32. D 33. C 34. E 35. D 36. E 37. B 38. B 39. A 40. B

Quantitative Aptitude 10. PROFIT AND LOSS

Quantitative Aptitude 10. PROFIT AND LOSS 10. PROFIT AND LOSS Cost Price: The price at which an article is purchased, is called the cost price or CP. Selling Price: The price at which an article is sold is called the selling price or SP. Formulae: