Father three times the son — Aptitude Question
Father three times the son: A father is three times as old as his son. In 12 years he will be twice as old. Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 50 seconds
Question
A father is three times as old as his son. In 12 years he will be twice as old. How old is the son now?
Options
- 10
- 12
- 14
- 16
Show the answer and the worked solution
Correct answer: B. 12
Worked solution
- Son = s, father = 3s.
- After 12 years: 3s + 12 = 2(s + 12) = 2s + 24, so s = 12.
- Check: 36 + 12 = 48 = 2 × 24. ✓
Answer: 12.
The idea
Write the present ages with one variable, shift both by the same number of years, and equate. The difference between two people's ages never changes — a quick check on any answer.
Shortcut. When the father is twice the son, the age gap equals the son's age. The gap is 2s now, so 2s = s + 12 and s = 12.
Common trap. Expanding 2(s + 12) as 2s + 12 — doubling the son's age but not the years added to it — gives s = 0, and a solver who then checks the options by eye can accept 14: father 42, then 54 against 26, which looks like twice but is 2 more than 2 × 26.