Mixture & Alligation

Ladakh Police Constable · Mathematics · 47 practice questions with answers and explanations: 8 Easy, 33 Medium, 6 Hard.

Sample questions

Sample Easy question 1

A mixture of milk and water is in the ratio 5:2. If the total is 35 litres, find the quantity of water.

  1. 8 litres
  2. 12 litres
  3. 10 litres
  4. 9 litres
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Answer: C. Water = (2/7) × 35 = 10 litres.

Sample Easy question 2

A mixture of sugar solution has sugar and water in the ratio 3:7. If the total is 50 litres, find the quantity of sugar.

  1. 20 litres
  2. 18 litres
  3. 15 litres
  4. 12 litres
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Answer: C. Sugar = (3/10) × 50 = 15 litres.

Sample Easy question 3

20 litres of milk is mixed with 5 litres of water. Find the percentage of water in the mixture.

  1. 20%
  2. 15%
  3. 25%
  4. 18%
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Answer: A. Total mixture = 25 litres. Water percentage = 5/25 × 100 = 20%.

Sample Medium question 4

A vessel contains 20 litres of milk. If 4 litres is replaced with water, how much pure milk is left?

  1. 17
  2. 15
  3. 16
  4. 14
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Answer: C. 20 - 4 = 16 litres of milk remain.

Sample Medium question 5

A 60-litre mixture of milk and water is in the ratio 2:1. How much water should be added to make the ratio 1:2?

  1. 50
  2. 70
  3. 40
  4. 60
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Answer: D. Milk = 40, water = 20. For a 1:2 ratio, water must equal 2 × 40 = 80, so 60 litres must be added.

Sample Medium question 6

Two alcohol solutions of 20% and 50% are mixed to make 30 litres of 30% solution. Find the quantity of the 20% solution used.

  1. 15
  2. 20
  3. 22
  4. 18
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Answer: B. By alligation: (50-30):(30-20) = 2:1, so 20% solution = (2/3) × 30 = 20 litres.

Sample Hard question 7

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.

Sample Hard question 8

Milk and water are in a vessel in the ratio 4:1. If 10 litres of the mixture is replaced with pure water, the ratio becomes 2:3. Find the initial quantity of the mixture.

  1. 15
  2. 22
  3. 20
  4. 18
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Answer: C. Solving with total = 5x litres gives x = 4, so the initial quantity was 20 litres.

Sample Hard question 9

A jar has liquids A and B in the ratio 4:1. When 10 litres of the mixture is removed and replaced with liquid B, the ratio becomes 2:3. Find the initial quantity of liquid A.

  1. 14
  2. 16
  3. 12
  4. 18
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Answer: B. Solving with total = 5x litres gives x = 4, so the initial quantity of A (4x) was 16 litres.

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