Ratio & Proportion

Ladakh Police Sub-Inspector · 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 2 : 2, 4 : 5 and 7 : 7 in its simplest form.

  1. 5 : 5
  2. 4 : 5
  3. 5 : 4
  4. 4 : 6
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Answer: B. Multiply the antecedents and the consequents: (2 × 4 × 7) : (2 × 5 × 7) = 56 : 70 = 4 : 5.

Sample Easy question 2

Find the compound ratio of 3 : 9, 2 : 6 and 8 : 3 in its simplest form.

  1. 8 : 28
  2. 27 : 8
  3. 9 : 27
  4. 8 : 27
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Answer: D. Multiply the antecedents and the consequents: (3 × 2 × 8) : (9 × 6 × 3) = 48 : 162 = 8 : 27.

Sample Easy question 3

Rs. 360 is divided among A, B and C in the ratio 2:3:4. What is C's share?

  1. 140
  2. 160
  3. 120
  4. 180
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Answer: B. Total parts = 9, each part = 40. C's share = 4 × 40 = 160.

Sample Medium question 4

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 5

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 Medium question 6

If 4 men or 6 women can do a piece of work in the same number of days, find the ratio of the work efficiency of a man to a woman.

  1. 3:2
  2. 1:2
  3. 2:3
  4. 4:5
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Answer: A. Since 4 men = 6 women in total work output, man:woman efficiency = 6:4 = 3:2.

Sample Hard question 7

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.

Sample Hard question 8

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.

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