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Problems on Ages Questions with Solutions

Problems on Ages are really just algebra in disguise — assign a variable to one age, express every other age in terms of it, and the given relationship becomes a solvable equation. Here’s the approach, four fully worked examples, and a few to try yourself.

The approach, quickly

  • Assign a variable to one unknown age (usually the one appearing in the simplest ratio or relationship), then express every other age in the problem in terms of that same variable.
  • "A is twice as old as B" means A = 2B — translate sentences in the same subject-first order they’re written, not reversed.
  • For "after N years" or "N years ago" conditions, add or subtract N from EVERY person’s age in the problem, including the one already defined in terms of x — forgetting to adjust one person’s age is the most common mistake here.
  • When a ratio is given directly (like "ages are in the ratio 3 : 5"), use a single multiplier — 3x and 5x — rather than two separate unknowns. This turns the problem into one variable, solvable with just one more equation from the rest of the problem.

Worked examples

1. A father is 3 times as old as his son. After 12 years, the father will be twice as old as his son. Find their present ages.

Solution

  1. Let the son’s present age = x, so the father’s present age = 3x.
  2. After 12 years: father = 3x + 12, son = x + 12. Given: 3x + 12 = 2(x + 12) → 3x + 12 = 2x + 24 → x = 12.
  3. Son = 12, Father = 36. Check: after 12 years, father = 48, son = 24, and 48 = 2 × 24.

Answer: Son = 12 years, Father = 36 years

2. The present ages of A and B are in the ratio 4 : 5. Eight years ago, their ages were in the ratio 3 : 4. Find their present ages.

Solution

  1. Let A = 4x and B = 5x.
  2. Eight years ago: A − 8 = 4x − 8, B − 8 = 5x − 8. Given: (4x − 8) / (5x − 8) = 3 / 4.
  3. Cross-multiply: 4(4x − 8) = 3(5x − 8) → 16x − 32 = 15x − 24 → x = 8.
  4. A = 4 × 8 = 32, B = 5 × 8 = 40. Check: 8 years ago, A = 24, B = 32, and 24 : 32 = 3 : 4.

Answer: A = 32 years, B = 40 years

3. Five years ago, Rohan’s age was three times his daughter’s age. Ten years from now, Rohan’s age will be twice his daughter’s age. Find their present ages.

Solution

  1. Let the daughter’s present age = x and Rohan’s present age = y.
  2. Five years ago: y − 5 = 3(x − 5) → y = 3x − 10 … (1)
  3. Ten years from now: y + 10 = 2(x + 10) → y = 2x + 10 … (2)
  4. Setting (1) = (2): 3x − 10 = 2x + 10 → x = 20. Then y = 2(20) + 10 = 50.

Answer: Daughter = 20 years, Rohan = 50 years

4. The sum of the present ages of a mother and her daughter is 40 years. Five years ago, the mother’s age was 4 times the daughter’s age. Find their present ages.

Solution

  1. Let the daughter’s present age = x, so the mother’s present age = 40 − x.
  2. Five years ago: daughter = x − 5, mother = 35 − x. Given: 35 − x = 4(x − 5) → 35 − x = 4x − 20 → 55 = 5x → x = 11.
  3. Daughter = 11, Mother = 40 − 11 = 29. Check: 5 years ago, daughter = 6, mother = 24, and 24 = 4 × 6.

Answer: Daughter = 11 years, Mother = 29 years

Try these yourself

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

1. A mother is 4 times as old as her son. After 20 years, she will be twice as old as her son. Find their present ages.

Answer: Son = 10 years, Mother = 40 years

2. The present ages of P and Q are in the ratio 5 : 7. Six years ago, their ages were in the ratio 2 : 3. Find their present ages.

Answer: P = 30 years, Q = 42 years

3. Six years ago, a man was 4 times as old as his son. Six years from now, he will be twice as old as his son. Find their present ages.

Answer: Son = 12 years, Man = 30 years

Where this comes up

Problems on Ages 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.

Practice more Problems on Ages questions

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

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