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Ratio and problems on ages for SSC CHSL

"The ratio of a mother's age to her daughter's is 7 : 2; after 5 years it will be 8 : 3." Age problems and ratio questions are close cousins — both are solved by letting one "part" be x and writing a simple equation. How to handle ratios, combine them, divide amounts, and solve the standard age problems quickly, with worked examples and answers.

28 Sept 2026 3 min read

In this guide
  1. Ratio basics
  2. Combining ratios
  3. Coins
  4. Income and expenditure
  5. Problems on ages
  6. Using options
  7. Practice

Ratio questions and age problems look different but use the same tool: let one part be x and translate the words into an equation. Age problems have one extra fact that makes them easier: everyone ages at the same rate, so the difference between two people's ages never changes.

Ratio basics

  • A ratio 3 : 5 means the quantities are 3x and 5x for some x.
  • Dividing an amount in the ratio a : b gives a/(a + b) and b/(a + b) of it.

Worked example: Divide ₹2,700 between P and Q in the ratio 4 : 5.
Total parts = 9; one part = 300. P = ₹1,200, Q = ₹1,500.

Combining ratios

If A : B = 3 : 4 and B : C = 6 : 5, make B equal: A : B = 9 : 12 and B : C = 12 : 10.
A : B : C = 9 : 12 : 10.

Coins

Worked example: A bag has ₹1, 50-paise and 25-paise coins in the ratio 2 : 3 : 4. The total value is ₹135. How many 50-paise coins are there?
Values: 2x × ₹1 + 3x × ₹0.50 + 4x × ₹0.25 = 2x + 1.5x + x = 4.5x = 135 → x = 30.
Fifty-paise coins = 3x = 90.

Income and expenditure

Worked example: The incomes of A and B are in the ratio 5 : 4, and their expenditures in the ratio 3 : 2. If each saves ₹4,000, find their incomes.
Income 5x and 4x; expenditure 3y and 2y.
5x − 3y = 4,000 and 4x − 2y = 4,000.
From the second, y = 2x − 2,000. Substitute: 5x − 6x + 6,000 = 4,000 → x = 2,000.
Incomes: ₹10,000 and ₹8,000.

Problems on ages

Worked example: The present ages of a mother and her daughter are in the ratio 7 : 2. After 5 years, the ratio will be 8 : 3. Find their present ages.
(7x + 5)/(2x + 5) = 8/3 → 21x + 15 = 16x + 40 → 5x = 25 → x = 5.
Present ages: 35 and 10. Check: in 5 years they will be 40 and 15, and 40 : 15 = 8 : 3. ✓

Worked example: The ages of two siblings are in the ratio 3 : 5. Eight years ago the ratio was 1 : 3. Find their present ages.
(3x − 8)/(5x − 8) = 1/3 → 9x − 24 = 5x − 8 → x = 4.
Present ages: 12 and 20.

Using options

Age questions are often fastest by testing the options: check which pair fits both conditions.

Worked example: The sum of the ages of a father and son is 50. Five years ago, the father was 7 times as old as the son. Find their present ages.
Option (40, 10): five years ago, 35 and 5 → 35 = 7 × 5 ✓. Answer: 40 and 10.

Practice

  1. Divide ₹3,600 among A, B and C in the ratio 2 : 3 : 7.
  2. If A : B = 2 : 3 and B : C = 4 : 5, find A : B : C.
  3. The ratio of the ages of two people is 4 : 7. The sum of their ages is 66. Find the elder's age.
  4. Six years ago, the ratio of the ages of X and Y was 3 : 4. The sum of their present ages is 54. Find X's present age.
  5. The incomes of two people are in the ratio 3 : 2 and their expenditures in the ratio 5 : 3. If each saves ₹2,000, find their incomes.

Answers: 1. ₹600, ₹900, ₹2,100. 2. 8 : 12 : 15. 3. 42. 4. 24 (six years ago: 18 and 24, sum 42 + 12 = 54). 5. ₹12,000 and ₹8,000.

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 Staff Selection Commission website .

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