Finding B's time alone — Time & Work Aptitude Question
Finding B's time alone: A and B together can complete a work in 8 days. A alone takes 12 days. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 50 seconds
Question
A and B together can complete a work in 8 days. A alone takes 12 days. How long would B alone take?
Options
- 16 days
- 20 days
- 24 days
- 30 days
Show the answer and the worked solution
Correct answer: C. 24 days
Worked solution
- Combined rate = 1/8; A's rate = 1/12.
- B's rate = 1/8 − 1/12 = 3/24 − 2/24 = 1/24.
- B alone takes 24 days.
Answer: 24 days.
The idea
Rates add and subtract; times do not. Subtracting 8 from 12 would give 4, which is nonsense since B must be slower than the pair.
Shortcut. For the missing partner, time = product ÷ difference: 8 × 12 ÷ (12 − 8) = 96 ÷ 4 = 24 days.
Common trap. 20 days — adding the two times (8 + 12); rates subtract, but times do not.