Three times now, twice later — Aptitude Question
Three times now, twice later: A man is three times as old as his son. Fifteen years hence he will be twice as old. Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A man is three times as old as his son. Fifteen years hence he will be twice as old. What is the man's present age?
Options
- 36
- 40
- 45
- 48
Show the answer and the worked solution
Correct answer: C. 45
Worked solution
- 3s + 15 = 2(s + 15) = 2s + 30 → s = 15.
- Man = 45.
- Check: in 15 years, 60 and 30. ✓
Answer: 45.
The idea
Adding years to both sides is the mirror of subtracting them. Set the equation up in the present and shift once.
Shortcut. When one person is twice another, the gap equals the younger's age at that moment. The gap is 2s now and always, so in fifteen years 2s = s + 15 → s = 15, and the man is 45.
Common trap. Solving for the son and stopping — s = 15, the same figure as the fifteen years — answers for the wrong person; the man is three times that. Expanding 2(s + 15) as 2s + 15 is the other slip, and it leaves s = 0.