Ratio & Proportion

Ladakh Prison Department · Mathematics · 106 practice questions with answers and explanations: 61 Easy, 43 Medium, 2 Hard.

Sample questions

Sample Easy question 1

Find the compound ratio of 8 : 9, 7 : 6 and 4 : 5 in its simplest form.

  1. 112 : 135
  2. 112 : 136
  3. 113 : 135
  4. 135 : 112
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Answer: A. Multiply the antecedents and the consequents: (8 × 7 × 4) : (9 × 6 × 5) = 224 : 270 = 112 : 135.

Sample Easy question 2

Find the compound ratio of 9 : 4, 9 : 5 and 4 : 4 in its simplest form.

  1. 82 : 20
  2. 20 : 81
  3. 81 : 21
  4. 81 : 20
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Answer: D. Multiply the antecedents and the consequents: (9 × 9 × 4) : (4 × 5 × 4) = 324 : 80 = 81 : 20.

Sample Easy question 3

Find the compound ratio of 9 : 2, 2 : 8 and 4 : 9 in its simplest form.

  1. 1 : 2
  2. 1 : 3
  3. 2 : 1
  4. 2 : 2
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Answer: A. Multiply the antecedents and the consequents: (9 × 2 × 4) : (2 × 8 × 9) = 72 : 144 = 1 : 2.

Sample Medium question 4

If a:b = 5:6 and b:c = 9:11, find a:c.

  1. 13:22
  2. 14:22
  3. 15:20
  4. 15:22
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Answer: D. Scaling a:b to 15:18 and b:c to 18:22 gives a:c = 15:22.

Sample Medium question 5

The ratio of the ages of a father and son is 7:2. After 10 years, the ratio will be 9:4. Find the son's present age.

  1. 8
  2. 12
  3. 10
  4. 9
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Answer: C. Solving (7x+10)/(2x+10)=9/4 gives x=5, so son's age = 2×5 = 10.

Sample Medium question 6

A sum is divided among A, B, C in the ratio 1/2:1/3:1/4. Find the ratio in whole numbers.

  1. 3:2:1
  2. 5:4:3
  3. 4:3:2
  4. 6:4:3
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Answer: D. Using the LCM of 2,3,4 (=12), the ratio becomes 6:4:3.

Sample Hard question 7

A, B, and C invest Rs. 94,000 in a business in the ratio 2:3:4. After 6 months, C withdraws. If the year-end profit is Rs. 20,000, find C's approximate share (profit split by investment × time).

  1. 5000
  2. 6000
  3. 5714
  4. 5500
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Answer: C. Unit-months: A=24, B=36, C=24, total=84. C's share = 20000 × 24/84 ≈ 5714.

Sample Hard question 8

The incomes of A and B are in the ratio 5:7 and their expenditures are in the ratio 3:5. If each saves Rs. 1000, find A's income.

  1. 2400
  2. 2600
  3. 2300
  4. 2500
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Answer: D. Let income = 5x, 7x and expenditure = 3y, 5y. Solving 5x-3y=1000 and 7x-5y=1000 gives x=500, so A's income = 2500.

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