How the sum of ages grows — Aptitude Question
How the sum of ages grows: The sum of the present ages of a father and son is 60 years. Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 120 seconds
Question
The sum of the present ages of a father and son is 60 years. Six years ago the father's age was five times the son's. What will the son's age be after 6 years?
Options
- 12
- 14
- 18
- 20
Show the answer and the worked solution
Correct answer: D. 20
Worked solution
- Son = s, father = 60 − s.
- Six years ago: (60 − s − 6) = 5(s − 6) → 54 − s = 5s − 30 → 6s = 84 → s = 14.
- So the son is 14 now and the father 46. Check: six years ago they were 8 and 40, and 40 = 5 × 8. ✓
- After 6 years the son will be 14 + 6 = 20.
Answer: 20.
The idea
Use the sum to remove one variable, solve for the present, then step forward to the moment the question asks about.
Shortcut. Six years ago the sum was 60 − 12 = 48, split 5 : 1 into 40 and 8. The son is wanted twelve years after that: 8 + 12 = 20.
Common trap. 14 is the son's present age; the question asks for his age after six years, and stopping at the present gives it.