Twice now, three times before — Aptitude Question
Twice now, three times before: A is twice as old as B. Ten years ago A was three times as old as B. Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A is twice as old as B. Ten years ago A was three times as old as B. What is B's present age?
Options
- 15
- 18
- 20
- 25
Show the answer and the worked solution
Correct answer: C. 20
Worked solution
- 2b − 10 = 3b − 30 → b = 20.
- So B is 20 and A is 40.
- Check: ten years ago 30 and 10. ✓
Answer: 20.
The idea
Expand the bracket and collect terms. The answer is B's age, not A's — read the question again before choosing.
Shortcut. Since A = 2B, the gap equals B's present age b. Ten years ago A was three times B, so the gap was then 2(b − 10). Equate the two: b = 2b − 20 → b = 20.
Common trap. 15 tempts because it makes A a tidy 30, yet ten years back that is 20 and 5 — four times, not three. Only 20 (A 40, then 30 and 10) survives the check.