Mixture & Alligation

J&K Bank PO · Quantitative Aptitude · 86 practice questions with answers and explanations: 38 Easy, 42 Medium, 6 Hard.

Sample questions

Sample Easy question 1

A mixture of 50 litres of milk and 15 litres of water is made. What is the ratio of milk to water?

  1. 3 : 10
  2. 10 : 3
  3. 13 : 3
  4. 50 : 65
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Answer: B. Milk : water = 50 : 15 = 10 : 3.

Sample Easy question 2

In what ratio must rice at ₹20 per kg be mixed with rice at ₹30 per kg so that the mixture is worth ₹24 per kg?

  1. 4 : 2
  2. 3 : 2
  3. 2 : 3
  4. 20 : 30
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Answer: B. By alligation: cheaper : dearer = (30 − 24) : (24 − 20) = 6 : 4 = 3 : 2.

Sample Easy question 3

A mixture of 20 litres of milk and 10 litres of water is made. What is the ratio of milk to water?

  1. 20 : 30
  2. 1 : 2
  3. 2 : 1
  4. 3 : 1
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Answer: C. Milk : water = 20 : 10 = 2 : 1.

Sample Medium question 4

A shopkeeper mixes tea costing Rs. 20/kg with tea costing Rs. 30/kg. If he uses 10 kg of the Rs. 30/kg tea and wants an average cost of Rs. 24/kg, how much of the Rs. 20/kg tea should he use?

  1. 15 kg
  2. 12 kg
  3. 20 kg
  4. 18 kg
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Answer: A. Let quantity of Rs. 20 tea = x. (20x + 300)/(x + 10) = 24, giving 20x + 300 = 24x + 240, so 4x = 60, x = 15 kg.

Sample Medium question 5

A vessel contains a mixture of milk and water in the ratio 4:1. If 10 litres of water is added, the ratio becomes 2:1. Find the original quantity of milk.

  1. 20 litres
  2. 18 litres
  3. 16 litres
  4. 24 litres
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Answer: A. Let milk = 4x, water = x. (4x)/(x+10) = 2/1, giving 4x = 2x + 20, so x = 10. Milk = 4×10 = 20 litres.

Sample Medium question 6

A trader mixes two varieties of rice in the ratio 2:3, costing Rs. 15/kg and Rs. 20/kg respectively. Find the average cost per kg of the mixture.

  1. Rs. 18.5
  2. Rs. 17.5
  3. Rs. 18
  4. Rs. 17
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Answer: C. Average cost = (2×15 + 3×20)/5 = (30+60)/5 = 18.

Sample Hard question 7

A container has a mixture of two liquids A and B in the ratio 7:5. When 9 litres of the mixture is drawn off and replaced with liquid B, the ratio becomes 7:9. Find the initial quantity of liquid A.

  1. 19.25 litres
  2. 20 litres
  3. 22.75 litres
  4. 21 litres
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Answer: D. Let total = 12x (A=7x, B=5x). Removing 9L keeps the 7:5 ratio in the remainder: A left = 7x − 5.25, B left = 5x − 3.75, and after adding back 9L of B: (7x−5.25)/(5x+5.25) = 7/9. Solving gives x = 3, so A = 7×3 = 21 litres.

Sample Hard question 8

In what proportion must water be mixed with milk costing Rs. 40/litre so that after selling the mixture at the cost price, there is a profit of 25%?

  1. 1:5
  2. 1:4
  3. 1:6
  4. 1:8
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Answer: B. For a 25% profit by dilution, the cost price of the mixture should be 40/1.25 = 32 per litre. By alligation with water at Rs. 0: ratio of water:milk = (40-32):(32-0) = 8:32 = 1:4.

Sample Hard question 9

A vessel has liquids A and B in the ratio 7:5. When 9 litres of the mixture is drawn off and replaced with B, the ratio becomes 7:9. Find the vessel's total capacity.

  1. 30
  2. 24
  3. 36
  4. 40
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Answer: C. Solving with total = 12x litres gives x = 3, so total capacity = 36 litres.

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