Three pairs of workers — Time & Work Aptitude Question
Three pairs of workers: A and B together can do a work in 12 days, B and C in 15 days, and C and A in 20 days. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
A and B together can do a work in 12 days, B and C in 15 days, and C and A in 20 days. How long will all three together take?
Options
- 8 days
- 10 days
- 12 days
- 15 days
Show the answer and the worked solution
Correct answer: B. 10 days
Worked solution
- Sum of pair rates = 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5.
- This equals 2(A + B + C), so A + B + C = 1/10.
- All three together take 10 days.
Answer: 10 days.
The idea
Adding the three pair rates counts each person exactly twice, so halve the sum. This is the standard route into every three-worker question.
Shortcut. Take 60 units: the pairs do 5, 4 and 3 a day, which counts each person twice, so the trio does 12 ÷ 2 = 6 a day and needs 60 ÷ 6 = 10 days.
Common trap. 12 days — the fastest pair's time, as if adding C changed nothing; a third worker must make the job quicker than any pair.