Mixture & Alligation

LSSSSB Non-Technical · Mathematics · 47 practice questions with answers and explanations: 8 Easy, 33 Medium, 6 Hard.

Sample questions

Sample Easy question 1

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 Easy question 2

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 3

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 Medium question 4

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 5

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 Medium question 6

How many kg of sugar costing Rs. 40/kg must be mixed with 20 kg costing Rs. 30/kg to get a mixture worth Rs. 35/kg?

  1. 18
  2. 20
  3. 22
  4. 15
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Answer: B. Rs. 35 is exactly midway between 30 and 40, so equal quantities are needed: 20 kg.

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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