Ratio 5 : 7 now, 3 : 4 later — Aptitude Question
Ratio 5 : 7 now, 3 : 4 later: The ages of A and B are in the ratio 5 : 7. After 6 years the ratio becomes 3 : 4. Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
The ages of A and B are in the ratio 5 : 7. After 6 years the ratio becomes 3 : 4. What is A's present age?
Options
- 25
- 30
- 35
- 42
Show the answer and the worked solution
Correct answer: B. 30
Worked solution
- Let A = 5x, B = 7x.
- (5x + 6)/(7x + 6) = 3/4 → 20x + 24 = 21x + 18 → x = 6.
- A = 5 × 6 = 30.
- Check: 36/48 = 3/4. ✓
Answer: 30.
The idea
Introduce one variable through the ratio (5x, 7x), then cross-multiply the later ratio. One linear equation, one unknown.
Shortcut. Back-substitute: A = 30 makes B = 42, and six years on 36 : 48 = 3 : 4.
Common trap. 42 — B's present age (7 × 6), picked when the question asks for A's.