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Ratio and proportion for IBPS Clerk

Dividing money in a ratio, combining two ratios, changing a ratio by adding or removing, coins, and the classic income–expenditure question. Ratio runs through DI, partnership, mixtures and ages. The methods and why they work, six worked examples and eight practice questions.

1 Oct 2026 6 min read

In this guide
  1. The parts method, and why it works
  2. Combining ratios
  3. Proportion and the three proportionals
  4. Changing a ratio
  5. Coins and notes
  6. Worked examples
  7. Common mistakes
  8. Practice
  9. What to do next

A ratio compares two quantities of the same kind. 3 : 5 means that for every 3 parts of the first there are 5 parts of the second. It says nothing about the actual amounts until the question gives you one more fact, such as a total or a difference.

Ratio matters in the clerk exam more than its own question count suggests. DI questions ask for ratios, and partnership, mixtures, ages and profit sharing are all ratio questions in different clothes. If you can move comfortably between parts and amounts, a whole family of word problems becomes routine.

The parts method, and why it works

Treat a ratio a : b as a parts and b parts of one common unit, x. The quantities are then ax and bx. Any extra fact gives you x.

  • Total given: ax + bx = total, so one part x = total ÷ (a + b).
  • Difference given: bx − ax = difference, so x = difference ÷ (b − a).

This works because a ratio only fixes the proportion. Multiplying both terms by the same x keeps the ratio unchanged, and the extra fact picks the one value of x that fits.

Combining ratios

If A : B = 2 : 3 and B : C = 4 : 5, B has different numbers of parts in each ratio. Make B the same in both by scaling each ratio. The LCM of 3 and 4 is 12, so A : B = 8 : 12 and B : C = 12 : 15, giving A : B : C = 8 : 12 : 15.

Scaling is allowed because 2 : 3 and 8 : 12 are the same ratio.

Proportion and the three proportionals

a : b = c : d means a × d = b × c (product of the extremes equals product of the means).

TermDefinitionFormula
Fourth proportional to a, b, ca : b = c : dd = b × c ÷ a
Third proportional to a, ba : b = b : cc = b² ÷ a
Mean proportional of a, ba : m = m : bm = √(a × b)

Changing a ratio

When the same number x is added to or taken from both terms, set up (a + x) ÷ (b + x) = new ratio and cross-multiply. When different changes apply to each term, as in "4 boys leave and 4 girls join", write each term in parts first, then apply the change.

Coins and notes

With coins, the ratio of number of coins is not the ratio of value. Multiply each count-ratio term by the coin's value first.

Worked examples

Example 1. Divide ₹2,700 among A, B and C in the ratio 2 : 3 : 4.

  1. Total parts = 9. One part = 2,700 ÷ 9 = 300.
  2. Shares: ₹600, ₹900 and ₹1,200.

Example 2. A : B = 2 : 3 and B : C = 4 : 5. If the three together have ₹1,400, how much does A have?

  1. A : B : C = 8 : 12 : 15, as above. Total parts = 35.
  2. One part = 1,400 ÷ 35 = 40. A = 8 × 40 = ₹320.

Example 3. The incomes of A and B are in the ratio 4 : 5 and their expenses in the ratio 3 : 4. Each saves ₹2,000. Find their incomes.

  1. Incomes 4x and 5x; expenses 3y and 4y.
  2. 4x − 3y = 2,000 and 5x − 4y = 2,000.
  3. Multiply the first by 4 and the second by 3: 16x − 12y = 8,000 and 15x − 12y = 6,000. Subtract: x = 2,000.
  4. Incomes: ₹8,000 and ₹10,000. Check: expenses ₹6,000 and ₹8,000 (ratio 3 : 4), savings ₹2,000 each.

Example 4. What number must be added to each of 7 and 11 so that the ratio becomes 3 : 4?

  1. (7 + x) ÷ (11 + x) = 3 ÷ 4.
  2. 4(7 + x) = 3(11 + x), so 28 + 4x = 33 + 3x and x = 5.
  3. Check: 12 : 16 = 3 : 4.

Example 5. A bag has ₹1, 50-paise and 25-paise coins in the ratio 2 : 3 : 4. The total value is ₹180. How many coins of each kind are there?

  1. Value ratio = 2 × 1 : 3 × 0.5 : 4 × 0.25 = 2 : 1.5 : 1 = 4 : 3 : 2.
  2. Values: 180 × 4/9 = ₹80, 180 × 3/9 = ₹60, 180 × 2/9 = ₹40.
  3. Coins: 80 one-rupee coins, 120 fifty-paise coins, 160 twenty-five-paise coins, which is 80, 120 and 160. Check: 80 : 120 : 160 = 2 : 3 : 4.

Example 6. In a class, boys and girls are in the ratio 5 : 3. If 4 boys leave and 4 girls join, the ratio becomes 1 : 1. How many students were there originally?

  1. Boys 5x, girls 3x. Then 5x − 4 = 3x + 4, so x = 4.
  2. Boys 20, girls 12, total 32. Check: after the change, 16 boys and 16 girls.

Common mistakes

  • Dividing a total by one term of the ratio instead of the sum of the terms.
  • Combining A : B and B : C without making B equal first.
  • Treating the coin-count ratio as the value ratio.
  • Adding the same number to both terms and assuming the ratio stays the same. It does not: 1 : 2 becomes 2 : 3 when you add 1.

Practice

Set a 5-minute timer.

  1. Divide ₹900 in the ratio 4 : 5.
  2. A : B = 3 : 4 and B : C = 6 : 7. Find A : B : C.
  3. Find the third proportional to 4 and 6.
  4. Find the fourth proportional to 3, 5 and 12.
  5. Find the mean proportional of 8 and 18.
  6. Two numbers are in the ratio 5 : 7 and differ by 20. Find them.
  7. What number must be subtracted from each of 15 and 25 so that the ratio becomes 1 : 3?
  8. Two salaries are in the ratio 3 : 5. After a ₹2,000 rise for each, the ratio is 2 : 3. Find the original salaries.

Answers:

  1. ₹400 and ₹500. One part = 900 ÷ 9 = 100.
  2. 9 : 12 : 14. LCM of 4 and 6 is 12, so A : B = 9 : 12 and B : C = 12 : 14.
  3. 9. 6² ÷ 4 = 36 ÷ 4.
  4. 20. 5 × 12 ÷ 3.
  5. 12. √(8 × 18) = √144.
  6. 50 and 70. The difference is 2 parts = 20, so one part = 10.
  7. 10. (15 − x) ÷ (25 − x) = 1/3 gives 45 − 3x = 25 − x, so x = 10. Check: 5 : 15 = 1 : 3.
  8. ₹6,000 and ₹10,000. (3x + 2,000) ÷ (5x + 2,000) = 2/3 gives 9x + 6,000 = 10x + 4,000, so x = 2,000. Check: 8,000 : 12,000 = 2 : 3.

What to do next

  • Practise the parts method on ten questions until "one part = total ÷ sum of terms" is automatic.
  • Combine three-term ratios daily for a week.
  • Apply ratio in problems on ages and partnership.
  • Revisit mixtures and alligation, which is ratio with a weighted average.

A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Institute of Banking Personnel Selection website .

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