A alone, from the pairs — Time & Work Aptitude Question
A alone, from the pairs: A and B together take 12 days, B and C take 15 days, and all three together take 10 days. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
A and B together take 12 days, B and C take 15 days, and all three together take 10 days. How long would A alone take?
Options
- 24 days
- 30 days
- 36 days
- 60 days
Show the answer and the worked solution
Correct answer: B. 30 days
Worked solution
- A's rate = 1/10 − 1/15 = 3/30 − 2/30 = 1/30.
- A alone takes 30 days.
Answer: 30 days.
The idea
Subtract the pair that excludes the person you want from the all-three rate. Choosing the wrong pair is the only way to go wrong.
Shortcut. Take 30 units: the trio does 3 a day and B + C does 2, so A does 1 a day — 30 days. The A + B figure is never needed.
Common trap. 60 days — subtracting the wrong pair (1/10 − 1/12 = 1/60), which gives C's time, not A's.