# Profit & Loss And Ratio & Proportion

SET 1

 01. A milkman mixes 20L of water with 80L of milk. After selling one-fourth of this mixture, he adds a water to replenish the quantity that he has sold. What is the current proportion of water to milk ? (a) 2 : 3 (b) 1 : 2 (c) 1 : 3 (d) 3 : 4
 02. Using only 2, 5, 10, 25 and 50 paise coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs 1.01 to three different persons? (a) 19 (b) 20 (c) 17 (d) 18
 03. Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then, the ratio of the shorter side to the longer side is ? (a) 1:2 (b) 2:3 (c) 1:4 (d) 3:4
 04. Mayank, Mirza, Little and Jaspal bought a motorbike for \$60,000. Mayank paid one half of the sum of the amounts paid by the other boys, Mirza paid one third of the sum of the amounts paid by the other boys; and Little paid one fourth of the sum of the amounts paid by the other boys. How much did Jaspal has to pay ? (a) \$15,000 (b) \$13,000 (c) \$17,000 (d) None of these
 05. A piece of string is 40 cm long. It is cut into three pieces. The longest piece is 3 times as long as the middle-sized and the shortest piece is 23 cm shorter than the longest piece. Find the length of the shortest piece(in cm) ? (a) 27 (b) 5 (c) 4 (d) 9
 06. Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes ? (a) 2 Kg (b) 2.4 Kg (c) 2.5 Kg (d) None of these
 07. I have one rupees coins, fifty paise coins and twenty five paise coins. The number of coins are in the ratio 2.5 : 3 : 4. If total amount with me is Rs 210, find the number of one  rupee coins ? (a) 90 (b) 85 (c) 100 (d) 105
 08. After allowing a discount of 11.11% , a trader still makes a gain of 14.28%. At how many percent above the cost price does he mark on his goods ? (a) 28.56% (b) 35% (c) 22.22% (d) None of these
 09. A dealer buys dry fruits at Rs 100, Rs 80 and Rs 60 per kilogram. He mixes them in the ratio 3 : 4 : 5 by weight and sells at a profit of 50%. At what price per kilogram does he sell the dry fruit ? (a) Rs 80 (b) Rs 100 (c) Rs 95 (d) None of these
 10. Two liquids A and B are in the ratio 5 : 1 in container 1 and 1 : 3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio of 1 : 1 ? (a) 2 : 3 (b) 4 : 3 (c) 3 : 2 (d) 3 : 4
Answers : Find Detailed Solutions at the end of the the page.

 1 A 2 A 3 D 4 B 5 C 6 C 7 D 8 A 9 D 10 D
SET 2

 01. Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage? (a) 20% (b) 25% (c) 40% (d) 15%
 02. I sold two watches for Rs 300 each, one at the loss of 10% and the other at the profit of 10%.What is the percentage of loss(-) or profit(+) that resulted from transaction? (a) (+)10 (b) (-)1 (c) (+))1 (d) (-)10
 03. The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ration 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs 70,000 less. Find the original price of the diamond? (a) Rs 1.4 lakh (b) Rs. 2 lakh (c) Rs 1 lakh (d) Rs 2.1 lakh
 04. A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particular sticky bargainer. How much percent above the cost price were his wares listed? (a) 100% (b) 80% (c) 75% (d) 66.66%
 05. A man buys spirit at Rs 60 per litre, adds water to it and then sells at Rs 75  per litre. What is the ratio of spirit to water if his profit in the deal is 37.5%? (a) 9 : 1 (b) 10 : 1 (c) 11 : 1 (d) None of these
 06. Two oranges, three bananas and four apples cost Rs 15. Three oranges, two bananas and one apple cost Rs 10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay? (a) Rs 10 (b) Rs 8 (c) Rs 15 (d) Cannot be det..
 07. From each of two given numbers, half the smaller number is subtracted. Of the resulting numbers the larger one is three times as large as the smaller. What is the ratio of the two numbers ? (a) 2:1 (b) 3:1 (c) 3:2 (d) None of these
 08. The marked price of a table is Rs. 1200, which is 20% above the cost price. It is sold at a discount of 10% on the marked price. Find the profit percent. (a) 10% (b) 8% (c) 7.5% (d) 6%
 09. If the work done by (x-1) men in (x+1) days is to the work done by (x+2) men in (x-1)days is in the ratio 9:10, then the value of x is ? (a) 10 (b) 12 (c) 8 (d) 15
 10. A cask contains a mixture of 49 litres of wine and water in the proportion 5:2. How much water must be added to it so that the ratio of wine to water may be 7:4 ? (a) 3.5 (b) 6 (c) 7 (d) None of these
Answers : Find Detailed Solutions at the end of the the page.
 1 A 2 B 3 C 4 A 5 B 6 C 7 A 8 B 9 C 10 B
 1. As one-fourth of the solution (milk + water = 80L + 20L ) is sold, solution drawn out of it is 100 x (1/4)= 25 L Quantity of the milk drawn out = 25 x (4/5)= 20 L » Quantity of water drawn out= 5L Now adding  25 L of water, quantity of water = 20 – 5 + 25 = 40L Also, quantity of milk remaining= 80 – 20 = 60L Required ratio= 40 : 60= 2 : 3 (a)
 2. 78 = 50 + 10 + 10 + 2 + 2 + 2 + 2 = 7 69 = 50 + 10 + 5 + 2 + 2 = 5 1.01 = 50 + 25 + 10 + 10 + 2 + 2 + 2 = 7 Hence, Number of coins 7 + 5 + 7 = 19 Coins (a)
 4. Mayank paid 1/2 of the sum paid by the other three. Let the other three paid  \$x jointly, then Mayank paid x/2. So, x + x/2 = 60000 i.e. x = 40000. Hence Mayank paid \$20, 000. Likewise, Mirza and little paid \$15000 and \$12000 respectively. Hence, amount paid by Jaspal  \$(60, 000)-(20,000 + 15,000 + 12,000)=13,000
 5. Let the largest piece be 3x, then middle and shortest piece would be x and (3x – 23) respectively. or 3x + x + ( 3x – 23) = 40 i.e. x=9, therefore shortest piece= (3 x 9 – 23) = 4 (c)
 6. Let y kg of dry grapes is obtained. Then, solid part in fresh grapes = solid part in the dry grapes 0.10 x 20 = 0.8 x yy=2.5 Kg. (c)
 7. Ratio of number of one rupee, fifty paisa, twenty five paisa coins= 2.5 : 3 : 4 » Ratio of value of coins= 2.5 x 1 : 3/2 : 4/4  »  5 : 3 : 2 Let amount of Rs 1 coins, 50 paisa coins and 25 paisa coins be 5x, 3x and 2x respectively. So, 5x + 3x + 2x = 210(given) Hence, x=21 »Value of one rupee coins = number of one rupees coins = 21 x 5=105 (d)
 8. Let the CP be Rs. 100 then SP= Rs. 114.28 (Profit=14.28%) This SP is arrived after giving a discount of 11.11% on marked price. Hence if marked price = y Then, y x 0.8889=114.28  » x=128.56 which is 28.56 % more than the CP.
 9. Cost price of ( 3 + 4 + 5 )= 12Kg of fruits Rs.( 300 + 320 + 300)= Rs. 920 SP at a profit of 50% = Rs. 1380 SP of fruits per kg= 1380/12= Rs. 115
 1. Let the price of 100 cm of cloth be Rs 100, but he gets 120 cm of cloth for Rs 100. Hence, his actual cost for 1 cm = 100/120= Rs. 5/6 Now, instead of selling 100 cm, by cheating he sells 80 cm of cloth for the cost price of 100 cm of cloth. To calculate his profit, the cost price of 80 cm of cloth = 5/6 X 80= Rs. 66.66 Selling Price of 80 cm of cloth(actually 100 cm for the buyes) at a discount of 20%. = 100 x 0.8= Rs. 80 Hence Profit Percentage= (80-66.66) x 100/66.66 = 20.02% or 20 % approx. (a)
 2. In such case where SP of two items is same and loss % and profit % is also same, there is always a loss on such transaction and it is given by loss percentage= (10)2/100= 1%
 3. Let the weight of the diamond be 10x, then price the diamond will be k(10)2=k.100x2 where k is a constant. Weight of each piece= x, 2x, 3x and 4x Therefore, their price will be kx2, k4x2, k9x2 and k16x2 Total price of pieces = kx2(1 + 4 + 9 + 16) = 30kx2 Given, k.100.x2- k.30.x2= 70,000 or kx2=1,000 » Original price of diamond =k.100.x2 = 100 x 100=1,00,000
 4. Let the CP of the article be Rs x, since he earns a profit of 20%, Hence SP = 1.2x. It is given that he incurs loss by selling 16 articles at the cost of 12 articles. loss=(16-12)x100/16=25% » His selling price = SP x 0.75 Now, SP x 0.75= 1.2x SP=1.2x/0.75 = 1.6x This SP is arrived after giving a discount of 20% on MP. Hence, MP= 1.6x/0.8=2x. It means that article has been marked 100% above the cost price.
 6. 2O + 3B + 4A = 15   —- (1) 3O + 2B + A = 10     —- (2) Adding equation (i) and (ii), we get 5O + 5B + 5A = 25 or O + B + A = 5 » 3O + 3B + 3A = 3 x 5 = 15 (c)
 9. We can solve this problem by taking the different values of x=10, 12, 8, 15 (c)
 10. Initial wine= 35 litres Initial water = 14 litres Since, we want to create 7 : 4 mixture of wine and water by adding only water, it mean that the amount of wine is constant at 35 litres. Thus, 7 : 4 = 35 : 20 Hence, water required is 6 litres.
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