Quantitative Aptitude

Ratio and Proportion: Practice Questions with Answers

14 practice questions on Ratio and Proportion, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   If a : b = 3 : 4 and b : c = 8 : 9, find a : b : c.

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   Answer: a : b : c = 6 : 8 : 9

   Solution:

   1. The shared term is b. In the first ratio b = 4, in the second b = 8 — scale the first ratio so its b also becomes 8: multiply both terms of 3 : 4 by 2, giving 6 : 8.
   2. The second ratio already has b = 8, so it stays 8 : 9.
   3. Combined: a : b : c = 6 : 8 : 9.

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2. Q.2

   The present ages of A and B are in the ratio 3 : 5. After 6 years, the ratio of their ages becomes 2 : 3. Find A’s present age.

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   Answer: 18 years

   Solution:

   1. Let present ages be A = 3x and B = 5x.
   2. After 6 years: (3x + 6) / (5x + 6) = 2 / 3
   3. Cross-multiply: 3(3x + 6) = 2(5x + 6) → 9x + 18 = 10x + 12 → x = 6
   4. A’s present age = 3x = 18. Check: after 6 years, A = 24, B = 36, and 24 : 36 = 2 : 3.

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3. Q.3

   Find the mean proportional between 4 and 25.

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   Answer: 10

   Solution:

   1. The mean proportional b between a and c satisfies b = √(a × c).
   2. b = √(4 × 25) = √100
   3. = 10

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4. Q.4

   If x : y = 2 : 3, find the value of (3x + 2y) : (4x − y).

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   Answer: 12 : 5

   Solution:

   1. Let x = 2k and y = 3k for some k.
   2. 3x + 2y = 3(2k) + 2(3k) = 6k + 6k = 12k
   3. 4x − y = 4(2k) − 3k = 8k − 3k = 5k
   4. Ratio = 12k : 5k = 12 : 5

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5. Q.5

   15 workers can finish a job in 8 days. How many workers, working at the same rate, are needed to finish the same job in 5 days?

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   Answer: 24 workers

   Solution:

   1. For a fixed amount of work, the number of workers and the number of days are inversely proportional — more workers means fewer days needed.
   2. Workers × Days = constant = 15 × 8 = 120.
   3. For 5 days: Workers = 120 / 5 = 24.

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6. Q.6

   Which ratio is greater: 3 : 4 or 5 : 7?

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   Answer: 3 : 4 is greater

   Solution:

   1. Cross-multiply: compare 3 × 7 with 4 × 5.
   2. 3 × 7 = 21, and 4 × 5 = 20.
   3. Since 21 > 20, 3 : 4 is the greater ratio.

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7. Q.7

   Divide ₹720 between A and B in the ratio 5 : 4.

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   Answer: A gets ₹400, B gets ₹320

   Solution:

   1. Sum of ratio terms = 5 + 4 = 9
   2. A’s share = (5/9) × 720 = 400
   3. B’s share = (4/9) × 720 = 320
   4. Check: 400 + 320 = 720

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8. Q.8

   Two numbers are in the ratio 7 : 11. The smaller number is 49. Find the larger number.

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   Answer: 77. 49/7 = 7 is the common multiplier x; the larger number = 11 × 7.

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9. Q.9

   If a : b = 2 : 3 and b : c = 5 : 7, find a : b : c.

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   Answer: a : b : c = 10 : 15 : 21. Scale 2:3 by 5 and 5:7 by 3 so b = 15 in both.

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10. Q.10

    Divide ₹1,500 among A, B and C in the ratio 2 : 3 : 5.

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    Answer: A = ₹300, B = ₹450, C = ₹750. Sum of parts = 10; each part is (ratio term/10) × 1,500.

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11. Q.11

    Find the mean proportional between 9 and 16.

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    Answer: 12. √(9 × 16) = √144.

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12. Q.12

    12 men can complete a task in 9 days, working at a constant rate per person. In how many days will 18 men complete it?

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    Answer: 6 days. Men × Days = 108 (constant); 108/18 = 6.

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13. Q.13

    Two numbers are in the ratio 4 : 5. If their sum is 108, find the two numbers.

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    Answer: 48 and 60. Each part = 108/9 = 12; 4×12 and 5×12.

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14. Q.14

    Which ratio is greater: 7 : 9 or 11 : 13?

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    Answer: 11 : 13 is greater. Cross-multiply: 7×13 = 91 and 9×11 = 99; 99 > 91.

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