How long B alone would take — Time & Work Aptitude Question
How long B alone would take: A and B can do a work in 10 days, B and C in 15 days, and A and C in 12 days. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 120 seconds
Question
A and B can do a work in 10 days, B and C in 15 days, and A and C in 12 days. How long would B alone take?
Options
- 24 days
- 30 days
- 36 days
- 40 days
Show the answer and the worked solution
Correct answer: A. 24 days
Worked solution
- Sum of pair rates = 1/10 + 1/15 + 1/12 = 6/60 + 4/60 + 5/60 = 15/60 = 1/4.
- This is 2(A + B + C), so A + B + C = 1/8.
- B = (A + B + C) − (A + C) = 1/8 − 1/12 = 3/24 − 2/24 = 1/24.
- B alone takes 24 days.
Answer: 24 days.
The idea
Halve the sum of the pair rates to get the three-worker rate, then subtract the pair that excludes the person you want.
Shortcut. B's rate is half of (A + B) + (B + C) − (A + C). In 60 units that is (6 + 4 − 5) ÷ 2 = 2.5 a day, so 60 ÷ 2.5 = 24 days.
Common trap. 40 days — subtracting the wrong pair (1/8 − 1/10 = 1/40), which gives C's time, not B's.