Mixture & Alligation

JKSSB Junior Engineer (Mechanical) · 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

Rice costing Rs. 45 per kg is mixed with rice costing Rs. 55 per kg in the ratio 3 : 1 by weight. What is the cost price of the mixture per kg?

  1. Rs. 47 1/2
  2. Rs. 44 1/2
  3. Rs. 49 1/2
  4. Rs. 50
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Answer: A. Mean price = (45 × 3 + 55 × 1) ÷ (3 + 1) = 47 1/2.

Sample Medium question 5

Rice costing Rs. 40 per kg is mixed with rice costing Rs. 60 per kg in the ratio 1 : 3 by weight. What is the cost price of the mixture per kg?

  1. Rs. 50
  2. Rs. 57
  3. Rs. 52
  4. Rs. 55
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Answer: D. Mean price = (40 × 1 + 60 × 3) ÷ (1 + 3) = 55.

Sample Medium question 6

Rice costing Rs. 50 per kg is mixed with rice costing Rs. 60 per kg in the ratio 4 : 1 by weight. What is the cost price of the mixture per kg?

  1. Rs. 49
  2. Rs. 55
  3. Rs. 52
  4. Rs. 54
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Answer: C. Mean price = (50 × 4 + 60 × 1) ÷ (4 + 1) = 52.

Sample Hard question 7

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 8

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 9

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.

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