Mixture and Alligations Exercises

Abhishek Jain

1. In what proportion must a grocer mix wheat at Rs. 2.04 per kg and Rs. 2.88 per kg so as to make a mixture of worth Rs. 2.57 per kg? Ans: 3:4 2. A mixture of certain quantity of milk with 8 L of water is worth 45 paise per litre. If pure milk be worth 54 paise per litre, how much milk is there in the mixture? Ans: 40 L 3. A trader has 50 kg of pulses, part of which he sells at 8% profit and rest at 18% profit. He gains 14% on the whole. What is the quantity sold at 18% profit? Ans: 30 kg 4. A merchant has 2000 kg of rice, part of which he sells at 36% profit and the rest at 16% profit. He gains 28% on the whole. Find the quantity sold at 16% Ans: 800 kg 5. A butler stole wine from a butt of sherry which contained 80% of spirit and he replaced it by wine containing only 32% spirit. Then the butt was of 48% strength only. How much of the butt did he steal? Ans: 2/3

6. Two vessels P and Q contain wine and water in the ratios of 5:2 and 8:5, respectively. Find the ratio in which these mixtures are to be mixed to get a new mixture containing wine and water in the ratio of 9:4 Ans: 7:2 7. A container is filled with liquid, 6 part of which are water and 10 part milk. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half milk? Ans: 1/5 8. A butler stole wine from a butt of sherry which contains 15% of spirit and he replaced what he had stolen by wine containing 6% of spirit. The butt was then 9% strong only. How much of the butt did he stole? Ans: 2/3 9. Ravinas savings and expenditure are in the ratio of 2:3. Her income increases by 10%. Her expenditure also increases by 12%. By how many percent does her saving increase? Ans: 7% 10. In a zoo, there are lions and parrots. If counted, there are 100 heads and 290 legs. How many parrots are there? Ans: 55

11. 4 L are drawn from a container full of milk and is then filled with water. This operation is performed three more times. The ratio of the quantity of milk left in the container and that of water is 16:65. How much milk did the container hold initially? Ans: 12 L 12. A container contains a mixture of two liquids A and B in the ratio of 7:5. When a litre of mixture is drawn off and the container is filled is with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the container initially? Ans: 21 13. A can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of mixture and drawn off and can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially? Ans: 21 14. Prabodh bought 30 kg of rice at the rate of Rs. 8.50 per kg and 20 kg of rice at the rate of Rs. 9.00 per kg. He mixed the two. At what price (approx) per kg should he sell the mixture in order to get 20% profit Ans: Rs. 10.50 15. Prabhu purchased 30 kg of rice at the rate of Rs. 17.50 per kg and another30 kg rice at a certain rate. He mixed the two and sold the entire quantity at the rate of Rs. 18.60 per kg and made 20 per cent overall profit. At what price per kg

did he purchase the lot of another 30 kg rice? Ans: Rs. 13.50 16. Nikita bought 30 kg of wheat at the rate of Rs. 4.75 per kg 40 kg of wheat at the rate of Rs.4.25 per kg and mixed them. She sold the mixture at the rate of Rs. 4.45 per kg. Her total profit or loss in the transaction was Ans: Re. 1 loss 17. A mixture contains spirit and water in the ratio 3:2. If it contains 3 litres more spirit than water, the quantity of spirit in the mixture is Ans: 9 litres 18. A vessel contains 50 litres milk. The milkman delivers 10 litres to the first house and adds an equal quantity of water. He does exactly the same at the second and third house. What is the ratio of milk and water when he has finished delivering at the third house? Ans: 64:61 19. Several litres of acid were drawn off from a 54 litres vessel full of acid and an equal amount of water is added. Again the same volume of the mixture was drawn off and replaced by water. As a result, the vessel contained 24 litres of pure acid. How much acid was drawn off initially? Ans: 18 litres

20. A mixture of a certain quantity of milk with 16 litres of water is worth 90 paisa per litre. If pure milk be worth 108 paise per litre, how much milk in there is the mixture? Ans: 80 litres 21. A mixture of a certain quantity of milk with 32 litres of water is worth Rs. 1.50 per litre. If pure milk be worth Rs. 4.50 per litre, how much milk is there in the mixture? Ans: 16 litre 22. The amount of wheat @ Rs. 610 per quintal which should be added to 126 quintals of wheat costing Rs. 285 per quintal so that 20% may be gained by selling the mixture at Rs. 480 per quintal will be Ans: 50 kg 23. Three vessels contain equal mixtures of milk & water in the ratio 6:1, 5:2, & 3:1 respectively. If all the solutions are mixed together, the ratio of milk to water in the final mixture will be Ans: 65:19 24. To mix spirits worth Rs. 8, Rs. 6 and Rs. 3 per gallon for making a mixture worth Rs. 5 per gallon, how much of each quantity is to be taken? Ans: 1:1:2 25. Two equal containers are filled with a mixture of water and alcohol. One of them contains three times as much

alcohol as the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to alcohol is 3:2. Find the ratio of water to alcohol in each of the original containers Ans: 2:3, 4:1 26. A 100 litre solution of milk and water contains water and milk in the ratio 1:4. 10% of the solution is removed and replaced by milk twice, in succession. What would be the quantity of water in the resultant solution? Ans: 16.2 litres 27. A container contains 240 litres of wine. 80 litres is taken out of the container everyday and an equal quantity of water is put into it. Find the quantity of the wine that remains in the container at the end of the fourth day Ans: 47.40 litres 28. A can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of mixture are drawn off and can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially? Ans: 21 29. Prabodh bought 30 kg of rice at the rate of Rs. 8.50 per kg and 20 kg of rice at the rate of Rs. 9.00 per kg. He mixed the two. At what price (approx) per kg should he sell the mixture in order to get 20% profit? Ans: Rs. 10.50

30. Prabhu purchased 30kg of rice at the rate of Rs. 17.50 per kg and another 30 kg rice at a certain rate. He mixed the two and sold the entire quantity at the rate of Rs. 18.60 per kg and made 20 per cent overall profit. At what price per kg did he purchase the lot of another 30 kg rice? Ans: Rs. 13.50 31. In what ratio must two kinds of tea worth Rs. 18 and Rs. 28 per kg be mixed so that by selling the mixture at Rs. 32 per kg there may be a gain of 20%? Ans: 2:13 32. A grocer mixes 26 kg of tea which costs Rs. 20 a kg with 30 kg of tea which costs Rs. 36 a kg and sells the mixture at Rs. 30 a kg. His profit percent is Ans: 5% 33. Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1:1:2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will Ans: Rs. 175.50 34. Nikita bought 30 kg of wheat at the rate of Rs. 4.75 per kg, 40 kg of wheat at the rate of Rs. 4.25 per kg and mixed them. She sold the mixture at the rate of Rs. 4.45 per kg. Her total profit or loss in the transaction was Ans: Re. 1 loss

35. A mixture contains spirit and water in the ratio 3:2. If it contains 3 litres more spirit than water, the quantity of spirit in the mixture is Ans: 9 litres 36. A container contains 240 litres of wine. 80 litres is taken out of the container everyday and an equal quantity of water is put into it. Find the quantity of the wine that remains in the container at the end of the fourth day Ans: 47.40 litres 37. A vessel contains 50 litres milk. The milkman delivers 10 litres to the first house and adds an equal quantity of water. He does exactly the same at the second and third house. What is the ratio of milk and water when he has finished delivering at the third house? Ans: 64:61 38. Several litres of acid were drawn off from a 54 litres vessel full of acid and an equal amount of water is added. Again the same volume of the mixture was drawn off and replaced by water. As a result, the vessel contained 24 litres of pure acid. How much acid was drawn off initially? Ans: 18 litres 39. A mixture of a certain quantity of milk with 16 litres of water is worth 90 paise per litre. If pure milk be worth 108 paisa per litre, how much milk is there in the mixture? Ans: 80 litres

40. A mixture of a certain quantity of milk with 32 litres of water is worth Rs. 1.50 per litre. If pure milk be worth Rs. 4.50 per litre, how much milk is there in the mixture? Ans: 16 litres. 41. A person has a chemical of Rs. 50 per litre. In what ratio should water be mixed in that chemical so that after selling the mixture at Rs. 40 per litre he may get a profit of 50%? Ans: 8:7 42. A trader has 50 kg of pulses, part of which he sells at 8% profit and the rest of 18% profit. He gains 14% on the whole. What is the quantity sold at 18% profit? Ans: 30 kg 43. A lump of two metals weighting 18 grams is worth Rs. 87 but if their weights be interchanged, it would be worth Rs. 78.60. If the price of one metal be Rs. 6.70 per game, find the weight of the other metal in the mixture Ans: 8 g 44. In two alloys, copper and zinc are related in the ratios of 4:1 and 1:3. 10 kg of 1st alloy, 16 kg of 2nd alloy and some of pure copper are melted together. An alloy was obtained in which the ratio of copper to zinc was 3:2. Find the weight of the new alloy Ans: 35 kg

45. Fresh fruit contains 72% water and dry fruit contained 20% water. How much dry fruit from 100 kg of fresh fruit can be obtained? Ans: 35 kg 46. A mixture contains acid and water in the ratio of 1:4 and another contains them in the ratio 4:5. If we want a third mixture from the above ones with a ratio 2:7, the proportion in which the two varieties should be mixed is Ans: 10:1 47. Selling price of milk depends on the fat content of milk. Normal fat content in pure milk is 60% and normal selling price is Rs. 20 per litre. If the fat content falls below 55%, then the selling price decreases by 20%. A milk man procedures pure milk at Rs. 16 per litre. How much water as percentage of pure milk can be added so that his selling price is not affected? Ans: 9.09% 48. A certain product C is made of two ingredients A and B in the proportion of 2:5. The price of A is three times that of B. The overall cost of C is Rs. 5.20 per kg including labour charges of 80 paisa per kg. Find the cost of B per kg? Ans: Rs. 2.80 49. Two vessels A and B contain mixture of spirit and water. A mixture of 3 parts from A and 2 parts from B is found to contain 29% of spirit and a mixture of 1 part from A and 9 parts from B is found to contain 34% of spirit. Find the

percentage of spirit in A and B Ans: 35, 25 50. Two lumps composed of gold, silver and copper together weight 20 kg, one lump contains gold 75% and silver 31.25 grams per kg. The other contains gold 85% and silver 30 grams per kg. The total quantity of silver in two lumps is 617.5 grams. If the two lumps are melted and formed into one, what percent of gold will it contain? Ans: 78% 51. Three vessels whose capacities are as 5:3:2 are completely filled with milk mixed with water. The ratio of milk and water in the mixture of vessels are as 3:2, 2:1 and 3:1 respectively. Find the percentage of water in the new mixture obtained when 1/3 rd of first, 1/2 of second and 2/3 rd of the third vessels is taken out and mixed together Ans: 33.33% 52. The amount of wheat @ Rs. 610 per quintal which should be added to 126 quintals of wheat costing Rs. 285 per quintal so that 20% may be gained by selling the mixture at Rs. 480 per quintal will be Ans: 69 quintal 53. Three vessels contain equal mixtures of milk & water in the ratio 6:1, 5:2 & 3:1 respectively. If all the solutions are mixed together, the ratio of milk to water in the final mixture will be Ans: 65:19

54. To mix spirits worth Rs. 8, Rs. 6 and Rs. 3 per gallon for making a mixture worth Rs. 5 per gallon, how much of each quantity is to be taken? Ans: 1:1:2 55. 10 gallons are drawn from a cask full of wine. It is then filled with water. 10 gallons of the mixture are drawn and the cask is again filled with water. The quantity of wine now left in the cask to that of the water in it is 256:39. How much does the cask hold? Ans: 50 gallons 56. The ratio of kerosene to petrol in 100 kgs of adulterated petrol normally used by three wheelers 7:25. The amount of kerosene to be added to 100 kgs of adulterated petrol to make the ratio 9:25 is Ans: 6.25 kgs 57. In what proportion must water be mixed with milk to gain 20% by selling it at the cost price Ans: 1:6 58. The contents in the beakers A and B are 80 cm3 of sugar and 80 cm3 of sand respectively. Now 20 cm3 of sugar is taken out from A and put into B. After through mixing, 20 cm3 of the mixture is taken out from B and put into A. Find

the percentage of sand in the mixture in A Ans: 20% 59. Two equal containers are filled with a mixture of water and alcohol. One of them contains three times as much alcohol as the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to alcohol is 3:2. Find the ratio of water to alcohol in each of the original containers Ans: 2:3, 4:1 60. A 100 litre solution of milk and water in the ratio 1:4. 10% of the solution is removed and replaced by milk twice, in succession. What would be the quantity of water in the resultant solution? Ans: 16.2 litres 61. Alok bought 25 kg and 35 kg of a commodity @ Rs. 6 per kg and Rs. 7 per kg respectively. He mixed the two quantities and sold the mixture @ Rs. 6.75 per kg. How much is the overall gain/loss to him? Ans: 10 gain 62. Suresh purchased 20 kg of tea of one variety at Rs. 30 per kg and 30 kg of tea of another variety at Rs. 25 per kg. How much is the total profit? Ans: Rs. 25

63. How many litres of Rs. 16 per litre wine should a merchant add with 25 litres of Rs. 20 per litre wine, so that he earns 25% by selling the mixture at Rs. 22? Ans: 37.5 litres 64. Two vessels contain mixtures of milk and water. One contains 80% milk and the other contains 60% milk. The proportion in which they should be mixed to get liquid with 75% milk and 25% water is Ans: 3:1 65. Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water? Ans: 3:2 66. Two kinds of tea were prepared. In the first, 30 grams of sugar was mixed with 190 grams of tea. In the second, 40 grams of sugar was mixed with 270 grams of tea. Which tea would be sweeter? If the two kinds of tea are mixed together, determine the percentage of tea in the mixture Ans: Ist, 86 67. A mixture is composed of 4 parts of brandy and 1 part of water, 1 kg of water is added, and the resulting mixture 3 times as much brandy as water. Find the quantity of brandy in the original mixture Ans: 12 kg

68. A dishonest milkman mixed 1 litre of water for every 3 litres of milk and thus made up 36 litres of milk. If he now adds 15 litres of milk to the mixture, find the ratio of milk and water in the new mixture Ans: 14:3 69. A dishonest milkman purchased milk at Rs. 10 per litres and mixed 5 litres of water in it. By selling the mixture at the rate of Rs. 10 per litre he earns a profit of 25%. The quantity of the mixture that he had was? Ans: 25 litres 70. A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture Ans: 19:81 71. A container has a capacity of 20 gallons and is full of spirit. 4 gallons of spirit is drawn out and the container is again filled with water. This process is repeated 5 times. Find out how much spirit is left in the resulting mixture finally? Ans: 6 gallons 72. A vessel is full of refined oil. 1/4 of the refined oil is taken out and the vessel is filled with mustard oil. If the process is repeated 4 times and 10 litres of refined oil is

finally left in the vessel, what is the capacity of the vessel? Ans: litres 73. In what ratio should two qualities of coffee powder having the rates of Rs. 47 per kg and Rs. 32 per kg be mixed in order to get a mixture that would have a rate of Rs. 37 per kg? Ans: 1:2 74. A sum of Rs. 36.90 is made up of 90 coins that are either 20 paisa coins or 50 paisa coins. Find out how many 20 paisa coins are there in the total amount? Ans: 27 75. A discount grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and there by gains 25%. Find the percentage of adulterated fat in the mixtures assuming that adulterated fat is freely available Ans: 20% 76. A thief steals four gallons of liquid soap kept in a train compartments bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it is found that the ratio of the liquid soap now left in the container to that of the water in it is 36:13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period? Ans: 28 gallons

77. A mixture of 70 litres of alcohol and water contains 10% of water. How much water must be added to the above mixture to make the water 12.5% of the resulting mixture? Ans: 2 litres 78. A mixture of 20 litres of brandy and water contains 10% water. How much water should be added to it to increase the percentage of water to 25%? Ans: 4 litres 79. A merchant purchased two qualities of pulses at the rate of Rs. 200 per quintal and Rs. 260 per quintal. In 52 quintals of the second quality, how much pulse of the first quality should be mixed so that by selling the resulting mixture at Rs. 300 per quintal, he gains a profit of 25%? Ans: 26 quintals 80. A man buys milk at Rs. 8.5 per litre and dilutes it with water. He sells the mixture at the same rate and thus gains 11.11%. Find the quantity of water mixed by him in every litre of milk Ans: 0.111 litre 81. There are two mixtures of honey and water, the quantity of honey in them being 25% and 75% of the mixture. If 2 gallons of the first are mixed with 3 gallons of the second, what will be the ratio of honey to water in the new mixture? Ans: 11:9

82. There are two kinds of alloys of tin and copper. The first alloy contains tin and copper such that 93:33% of it is tin. In the second alloy there is 86.66% tin. What weight of the first alloy should be mixed with some weight of the second alloy so as to make containing 90% of tin? Ans: 25 kg 83. Two containers of equal capacity are full of a mixture of oil and water. In the first, the ratio of oil to water is 4:7 and in the second it is 7:11. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of oil to water? Ans: 149:247 84. Two vessels contain spirit and water mixed respectively in the ratio of 1:3 and 3:5. Find the ratio in which these are to be mixed to get a new mixture in which the ratio of spirit to water is 1:2 Ans: 1:2 85. A person purchased a cupboard and a cot for Rs. 18,000. He sold the cupboard at a profit of 20% and the cot at a profit of 30%. If his total profit was 25.833%, find the cost price of the cupboard Ans: Rs. 75,000 86. A vessel is full of a mixture of kerosene and petrol in which there is 18% kerosene. Eight litres are drawn off and then the vessel is filled with petrol. If the kerosene is now

15%, how much does the vessel hold? Ans: 48 litres 87. Two solutions of 90% and 97% purity are mixed resulting in 21 litres of mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture? Ans: 9 litres 88. What will be the ratio of petrol and kerosene in the final solution formed by mixing petrol and kerosene that are present in three vessels in the ratio 4:1, 5:2 and 6:1 respectively? Ans: 83:22 89. A mixture worth Rs. 3.25 a kg is formed by mixing two types of flour, one costing Rs. 3.10 per kg while the other Rs. 3.60 per kg. In what proportion must they have been mixed? Ans: 7:3 90. In what proportion must water be mixed with milk so as to gain 20% by selling the mixture at the cost price of the milk? (Assume that water is freely available) Ans: 1:5 a. 30 b. 30+ 10 c. 10 d. 60+ 20