Ratio & Proportion

LSSSSB Non-Technical · Mathematics · 106 practice questions with answers and explanations: 61 Easy, 43 Medium, 2 Hard.

Sample questions

Sample Easy question 1

If p:q = 5:6 and q:r = 2:3, find p:q:r.

  1. 6:7:8
  2. 3:4:5
  3. 4:5:6
  4. 5:6:9
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Answer: D. Scaling p:q to 10:12 and q:r to 12:18 gives p:q:r = 10:12:18 = 5:6:9.

Sample Easy question 2

A sum of Rs. 1200 is divided among A, B and C in the ratio 1:2:3. Find B's share.

  1. 420
  2. 380
  3. 350
  4. 400
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Answer: D. Total parts=6, each part=200, B's share = 2×200 = 400.

Sample Easy question 3

A sum is divided among A, B, C, D in the ratio 3:4:5:6. If D gets Rs. 150 more than A, find the total sum.

  1. 920
  2. 900
  3. 880
  4. 850
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Answer: B. D-A = 3 parts = 150, so each part = 50; total (18 parts) = 900.

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

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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