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Ratio and Proportion Questions with Solutions

Ratio and Proportion is foundational — ages, mixtures, partnerships and even some Profit and Loss questions all lean on it. Here’s the concept, four fully worked examples, and a few to try yourself.

The concept, quickly

  • A ratio a : b compares two quantities of the same kind and has no units. Multiplying or dividing both terms by the same non-zero number gives an equivalent ratio.
  • A proportion is two equal ratios: a : b = c : d, which means a × d = b × c ("product of extremes = product of means") — this cross-multiplication is how most proportion questions get solved.
  • To split a total T in the ratio a : b : c, each part = (that term ÷ sum of terms) × T.
  • To combine two ratios a : b and b : c that share a term into one three-term ratio a : b : c, scale each ratio so the shared term (b) matches in both, usually by finding their LCM.

Worked examples

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

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

Answer: A gets ₹400, B gets ₹320

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

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.

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

3. 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.

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.

Answer: 18 years

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

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

Answer: 12 : 5

Try these yourself

Work through these the same way, then check against the answer.

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

Answer: A = ₹300, B = ₹450, C = ₹750

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

Answer: a : b : c = 10 : 15 : 21

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

Answer: 48 and 60

Where this comes up

Ratio and Proportion is tested directly in the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — and the same idea underlies ages, mixtures and partnership questions.

Practice more Ratio and Proportion questions

This page covers the concept and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Ratio and Proportion (and every other Quant/Reasoning/English topic) with instant scoring and explanations — free, no account required.

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