Twice as old, five years ago — Aptitude Question
Twice as old, five years ago: Five years ago A was twice as old as B. Their present ages are in the ratio 9 : 5. Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
Five years ago A was twice as old as B. Their present ages are in the ratio 9 : 5. What is A's present age?
Options
- 36
- 40
- 45
- 54
Show the answer and the worked solution
Correct answer: C. 45
Worked solution
- 9k − 5 = 2(5k − 5) = 10k − 10 → k = 5.
- A = 9 × 5 = 45 and B = 25.
- Check: five years ago 40 and 20. ✓
Answer: 45.
The idea
The present ratio supplies the variable and the past condition the equation. Expanding the bracket before collecting keeps the signs straight.
Shortcut. A's age must be a multiple of 9: 36, 45 or 54. Test 45: B is 25, and five years back 40 and 20 — exactly twice. 36 gives 31 and 15, which fails.
Common trap. 40 is A's age five years ago (2 × 20); solving correctly and quoting the past age instead of the present one gives it.