Three times now, four times then — Aptitude Question
Three times now, four times then: A father is three times as old as his son. Five years ago he was four times as old. Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A father is three times as old as his son. Five years ago he was four times as old. What is the father's present age?
Options
- 40
- 45
- 48
- 50
Show the answer and the worked solution
Correct answer: B. 45
Worked solution
- Son = s, father = 3s.
- 3s − 5 = 4(s − 5) = 4s − 20 → s = 15.
- Father = 3 × 15 = 45.
- Check: five years ago 40 and 10, and 40 = 4 × 10. ✓
Answer: 45.
The idea
One variable for the present, then shift both ages by the same number of years. The age difference never changes, which is a fast check on any answer.
Shortcut. The father's age must be a multiple of 3, which leaves 45 and 48. Test 45: son 15, and five years back 40 and 10 — exactly four times. 48 gives 43 and 11, which fails.
Common trap. 40 is the father's age five years ago (4 × 10). Solving correctly and then reading off the past age instead of the present one produces it.