Ratio & Proportion

Ladakh Police Constable · 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 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 Easy question 2

Find the compound ratio of 5 : 8, 2 : 5 and 5 : 8 in its simplest form.

  1. 5 : 33
  2. 32 : 5
  3. 5 : 32
  4. 6 : 32
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Answer: C. Multiply the antecedents and the consequents: (5 × 2 × 5) : (8 × 5 × 8) = 50 : 320 = 5 : 32.

Sample Easy question 3

Find the compound ratio of 5 : 8, 3 : 6 and 8 : 9 in its simplest form.

  1. 18 : 5
  2. 5 : 18
  3. 6 : 18
  4. 5 : 19
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Answer: B. Multiply the antecedents and the consequents: (5 × 3 × 8) : (8 × 6 × 9) = 120 : 432 = 5 : 18.

Sample Medium question 4

If a:b = 5:6 and b:c = 4:7, find a:c.

  1. 11:21
  2. 9:21
  3. 10:21
  4. 8:21
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Answer: C. a:c = (5×4):(6×7) = 20:42 = 10:21.

Sample Medium question 5

If x:y = 3:4, find (2x+3y):(3x+2y).

  1. 18:17
  2. 17:16
  3. 19:18
  4. 16:15
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Answer: A. With x=3k, y=4k: 2x+3y=18k, 3x+2y=17k, giving a ratio of 18:17.

Sample Medium question 6

Find the mean proportion between 9 and 16.

  1. 12
  2. 10
  3. 11
  4. 13
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Answer: A. Mean proportion = √(9×16) = √144 = 12.

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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