A father said to his son, “n years back I was as old as you are now. My present age is four times your age n years back”. If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages?
Answer & explanation
Answer: (a) 30 years
n years ago the father was the son’s present age, so n is the gap between their ages. Using ‘father now = 4 × son n years ago’ gives father : son = 8 : 5, so with a total of 130 they are 80 and 50, a difference of 30 years.
- Let the father’s age be F and the son’s S. ‘n years back I was as old as you are now’: F − n = S, so n = F − S.
- Son’s age n years back = S − n = S − (F − S) = 2S − F.
- F = 4(2S − F) → 5F = 8S → F : S = 8 : 5.
- F + S = 130 → 13 parts = 130 → 1 part = 10, so F = 80 and S = 50.
- Difference = 80 − 50 = 30 years.
- Check: n = 30; the son was 20 thirty years ago, and 4 × 20 = 80.
Remember · ‘I was your present age n years ago’ means n equals the age gap; turn the rest into a ratio.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·