Mixture & Alligation

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

Sample questions

Sample Easy question 1

In what ratio should water (free) be mixed with milk to gain 25% by selling the mixture at the cost price of milk?

  1. 1:5
  2. 1:3
  3. 1:6
  4. 1:4
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Answer: D. To gain 25% by diluting with free water, the required ratio of water to milk is 1:4.

Sample Easy question 2

A 60-litre mixture has milk and water in the ratio 5:1. Find the quantity of milk.

  1. 48
  2. 52
  3. 45
  4. 50
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Answer: D. Milk = (5/6) × 60 = 50 litres.

Sample Easy question 3

A 50-litre mixture contains milk and water in the ratio 4:1. Find the quantity of water.

  1. 12
  2. 9
  3. 10
  4. 8
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Answer: C. Water = (1/5) × 50 = 10 litres.

Sample Medium question 4

How much water should be added to 60 litres of a solution containing 40% acid to reduce the acid concentration to 25%?

  1. 30 litres
  2. 34 litres
  3. 36 litres
  4. 32 litres
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Answer: C. Acid quantity = 24 litres (constant). For 25% concentration: 24/(60+x) = 0.25, giving 60+x = 96, so x = 36 litres.

Sample Medium question 5

A vessel contains 60 litres of a mixture of milk and water in the ratio 2:1. 15 litres of the mixture is removed and replaced with 15 litres of water. Find the new ratio of milk to water.

  1. 5:4
  2. 1:1
  3. 3:2
  4. 2:1
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Answer: B. Initial milk = 40, water = 20. Removing 15L mixture removes 10L milk and 5L water (in the 2:1 ratio), leaving 30 milk and 15 water. Adding 15L water gives 30 milk, 30 water — a ratio of 1:1.

Sample Medium question 6

A vessel contains 40 litres of pure milk. 8 litres is removed and replaced with water, and this process is repeated once more. Find the quantity of milk left after the second replacement.

  1. 26.4 litres
  2. 24.8 litres
  3. 24 litres
  4. 25.6 litres
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Answer: D. After each replacement, the remaining fraction is (1 - 8/40) = 0.8. After 2 replacements: 40 × 0.8² = 40 × 0.64 = 25.6 litres.

Sample Hard question 7

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 8

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.

Sample Hard question 9

Two vessels contain milk and water in the ratios 2:3 and 5:3 respectively. In what ratio should quantities from the two vessels be mixed to get an equal (1:1) ratio of milk to water?

  1. 4:5
  2. 3:5
  3. 5:3
  4. 5:4
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Answer: D. Milk fractions are 0.4 and 0.625; by alligation for a target of 0.5, the ratio is (0.625-0.5):(0.5-0.4) = 5:4.

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