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← Index: Mixtures & Alligation — Complete Exam GuideChapter 15
Study Guide · Chapter 15

6. Practice Question Set B — Moderate / Exam Level

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  1. A container contains 40 litres of milk. From this container, 4 litres of milk was taken out and replaced with water. This process was repeated two more times. How much milk is now contained in the container? (Repeated replacement)
  1. 26.62 L (b) 27.36 L (c) 28.5 L (d) 29.16 L
  1. A mixture contains milk and water in the ratio 5:3. If 16 litres of water is added to the mixture, the ratio of milk to water becomes 5:4. Find the quantity of milk in the mixture. (Ratio-equation)
  1. 70 L (b) 75 L (c) 80 L (d) 85 L
  1. Three glasses of equal volume contain acid mixed with water in the ratios 1:2, 2:3 and 4:1 respectively. The contents of all three glasses are poured into a single vessel. Find the resultant ratio of acid to water. (Mixture of 3+ mixtures)
  1. 22:23 (b) 23:22 (c) 11:12 (d) 12:11
  1. A vessel is filled with a liquid, 3 parts of which are water and 5 parts are syrup. How much of the mixture must be drawn off and replaced with water so that the resulting mixture is half water and half syrup? (Replacement with target concentration)
  1. 1/8 (b) 1/5 (c) 1/4 (d) 1/3
  1. The average salary of all employees in a company is Rs 12,000. The average salary of officers is Rs 30,000 and of non-officers is Rs 10,000. If the number of officers is 60, find the number of non-officers. (Alligation on averages)
  1. 480 (b) 500 (c) 540 (d) 600
  1. A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. Find the quantity sold at 18% profit. (Alligation on profit %)
  1. 400 kg (b) 500 kg (c) 600 kg (d) 700 kg
  1. Milk costing Rs 20/L is to be mixed with water so that, after selling the mixture at Rs 20/L, the seller gains 25%. Find the ratio of milk to water. (Alligation + profit, free ingredient)
  1. 3:1 (b) 4:1 (c) 1:4 (d) 5:1
  1. A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another whisky containing 19% alcohol, and now the percentage of alcohol is found to be 26%. Find the fraction of the whisky that was replaced. (Replacement formula, concentration version)
  1. 1/3 (b) 2/3 (c) 3/4 (d) 1/2
  1. 300 g of a sugar solution has 40% sugar in it. How much sugar should be added to make it 50% sugar? (Concentration change on addition)
  1. 40 g (b) 50 g (c) 60 g (d) 75 g
  1. Vessels A and B contain spirit and water mixed in the ratio 5:2 and 7:6 respectively. Find the ratio in which these mixtures should be mixed to get a new mixture in vessel C containing spirit and water in the ratio 8:5. (Reverse alligation on mixtures)
  1. 7:9 (b) 9:7 (c) 5:8 (d) 8:5
  1. A container has milk and water in the ratio 4:3. If 21 litres of the mixture is removed and replaced with water, the new ratio of milk to water becomes 2:3. Find the initial quantity of the mixture. (Replacement, find original quantity)
  1. 56 L (b) 63 L (c) 70 L (d) 77 L
  1. A can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of the mixture are drawn off and the can is filled with liquid B, the ratio of A to B becomes 7:9. How many litres of liquid A were in the can initially? (Classic replacement, find component quantity)
  1. 18 L (b) 21 L (c) 23 L (d) 25 L
  1. A trader mixed 90 kg of rice at Rs 15/kg with some rice at Rs 19/kg and sold the mixture at Rs 20/kg, making a profit of 25%. Find the quantity of rice mixed at Rs 19/kg. (Alligation + profit, find quantity)
  1. 25 kg (b) 30 kg (c) 35 kg (d) 40 kg
  1. The distance covered by a train in the first half of a journey is covered at 40 km/hr and the second half (equal distance) at 60 km/hr. What is the average speed for the whole journey? (Average speed — equal distance, harmonic mean; tests common mistake)
  1. 48 km/hr (b) 50 km/hr (c) 45 km/hr (d) 52 km/hr
  1. A container contains a mixture of two liquids P and Q in the ratio 5:3. If 16 litres of the mixture is replaced with liquid Q, the ratio becomes 3:5. Find the initial quantity of liquid P. (Replacement, find component quantity)
  1. 20 L (b) 24 L (c) 25 L (d) 30 L
  1. In what ratio must three varieties of oil costing Rs 40/L, Rs 60/L and Rs 100/L be mixed to get a mixture costing Rs 76/L, given that equal quantities of the first two varieties are used? (Three-ingredient alligation with extra condition)
  1. 3:3:7 (b) 6:6:13 (c) 4:4:9 (d) 5:5:11
  1. A container contains 256 L of pure alcohol. Every time, one-fourth of the mixture present is withdrawn and replaced with an equal quantity of water. After how many such operations will the quantity of alcohol in the container reduce to 81 L? (Reverse replacement — find n)
  1. 3 (b) 4 (c) 5 (d) 6
  1. A vessel contains 128 L of pure milk. A certain quantity is withdrawn and replaced with water, and the operation is repeated 2 more times (3 times in total). If 54 L of milk remains at the end, find the quantity withdrawn each time. (Reverse replacement — find x)
  1. 24 L (b) 28 L (c) 32 L (d) 36 L
  1. A mixture of 40 L contains milk and water in the ratio 3:1. How many litres of the mixture must be drawn off and replaced with pure milk so that the new mixture contains milk and water in the ratio 9:1? (Replacement with the pure ingredient)
  1. 16 L (b) 20 L (c) 24 L (d) 28 L
  1. The average age of 40 students in a class is 15 years. When the class teacher’s age is included, the average age increases to 16 years. Find the teacher’s age. (Alligation on averages)
  1. 45 years (b) 50 years (c) 55 years (d) 56 years
  1. A merchant mixes rice worth Rs 12/kg with rice worth Rs 18/kg to prepare a mixture. He sells the mixture at Rs 20/kg, earning a profit of 25%. Find the ratio in which the two varieties were mixed. (Alligation + profit, reverse)
  1. 1:2 (b) 2:1 (c) 1:3 (d) 3:1
  1. Vessel A contains 15 L of a milk-water mixture in the ratio 2:1. Vessel B contains 25 L of a mixture with an unknown milk-water ratio. When mixed, the resultant 40 L mixture has milk and water in the ratio 3:2. Find the ratio of milk to water in vessel B. (Reverse — unknown ratio inside one vessel)
  1. 11:14 (b) 14:11 (c) 12:13 (d) 13:12
  1. A car travels a certain distance at 30 km/hr, an equal distance at 60 km/hr, and an equal further distance at 20 km/hr. Find the average speed for the entire journey. (Average speed — equal distances, harmonic mean, three legs)
  1. 30 km/hr (b) 35 km/hr (c) 36 km/hr (d) 40 km/hr
  1. A milkman sells milk mixed with water at the cost price of pure milk, thereby gaining 9(1)/(11)%. Find the percentage of water in the mixture. (Dishonest dealer, fractional gain%)
  1. 8.33% (b) 9.09% (c) 7.69% (d) 10%
  1. A tank contains a solution which is 81% pure milk. If 20% of the solution is replaced by water, and this process is repeated twice more (3 times in total), what will be the percentage of milk in the final solution? (Repeated replacement on percentage directly)
  1. 41.47% (b) 45.33% (c) 38.88% (d) 50%
  1. A shopkeeper mixes 20 kg of pulses costing Rs 15/kg with 30 kg of pulses costing Rs 25/kg, and sells the entire mixture at Rs 25.20/kg. Find his profit percentage. (Alligation + profit%, direct)
  1. 15% (b) 18% (c) 20% (d) 25%
  1. A vessel contains a mixture of acid and water in the ratio 3:2. If 10 litres of the mixture is replaced with water, the ratio becomes 2:3. Find the initial quantity of the mixture. (Replacement, find total quantity)
  1. 25 L (b) 30 L (c) 35 L (d) 40 L
  1. Three containers of capacities 20 L, 30 L and 40 L are filled with mixtures of milk and water in the ratios 3:1, 4:1 and 5:3 respectively. If all three mixtures are combined, find the percentage of water in the final mixture. (Mixture of 3 unequal-volume mixtures — percentage form)
  1. 25% (b) 26(1)/(2)% (c) 28(8)/(9)% (d) 30%
  1. Alloy A contains copper and zinc in the ratio 5:3. Alloy B contains copper and zinc in the ratio 1:3. In what ratio should A and B be mixed so that the resulting alloy has copper and zinc in equal proportion? (Alligation applied to alloys)
  1. 1:2 (b) 2:1 (c) 3:2 (d) 2:3
  1. A shopkeeper wants to prepare 35 kg of a mixture worth Rs 58/kg by mixing pulses costing Rs 50/kg and Rs 70/kg. He then sells the entire mixture to earn an overall profit of 15%. Find (i) the ratio in which the two varieties should be mixed, and (ii) the selling price per kg. (Alligation + profit%, combined)
  1. 3:2, Rs 66.70 (b) 2:3, Rs 65 (c) 3:2, Rs 65.50 (d) 2:3, Rs 66.70
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