Mixture & Alligation

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

Sample questions

Sample Easy question 1

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 Easy question 2

In a mixture of 40 litres, milk and water are in the ratio 3:1. How much water should be added to make the ratio 3:2?

  1. 10 litres
  2. 12 litres
  3. 9 litres
  4. 8 litres
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Answer: A. Milk = 30 litres, water = 10 litres. For ratio 3:2 with milk fixed at 30, water needed = 20 litres, so 10 more litres must be added.

Sample Easy question 3

A mixture of milk and water is in the ratio 3:1. If the total mixture is 40 litres, find the quantity of water.

  1. 8
  2. 10
  3. 12
  4. 9
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Answer: B. Water = (1/4) × 40 = 10 litres.

Sample Medium question 4

In what ratio must a shopkeeper mix tea costing Rs. 20/kg with tea costing Rs. 30/kg to get a mixture costing Rs. 24/kg?

  1. 2:3
  2. 3:2
  3. 1:1
  4. 4:1
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Answer: B. By alligation: ratio = (30-24):(24-20) = 6:4 = 3:2.

Sample Medium question 5

In what ratio must rice costing Rs. 40/kg be mixed with rice costing Rs. 60/kg to get a mixture costing Rs. 45/kg?

  1. 3:1
  2. 3:2
  3. 2:3
  4. 1:3
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Answer: A. By alligation: ratio = (60-45):(45-40) = 15:5 = 3:1.

Sample Medium question 6

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 Hard question 7

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 8

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.

Sample Hard question 9

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.

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