Ratio 6 : 5 now, 9 : 8 later — Aptitude Question
Ratio 6 : 5 now, 9 : 8 later: The ages of A and B are in the ratio 6 : 5. After 15 years the ratio becomes 9 : 8. Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
The ages of A and B are in the ratio 6 : 5. After 15 years the ratio becomes 9 : 8. What is A's present age?
Options
- 25
- 30
- 36
- 40
Show the answer and the worked solution
Correct answer: B. 30
Worked solution
- (6x + 15)/(5x + 15) = 9/8 → 48x + 120 = 45x + 135 → 3x = 15 → x = 5.
- A = 6 × 5 = 30.
- Check: in 15 years, 45 and 40, and 45/40 = 9/8. ✓
Answer: 30.
The idea
A ratio supplies the variable; the later ratio supplies the equation. Cross-multiply and solve — it is always linear.
Shortcut. Both ratios have a gap of one part (6 − 5 and 9 − 8), and the gap in years never changes, so the part size is the same: 6x + 15 = 9x → x = 5, A = 30.
Common trap. 25 is B's present age (5 × 5): x is found correctly and then substituted into the wrong person's ratio term.