Single correct option
A and B together can finish a job in 10 days, B and C together in 12 days, and C and A together in 20 days. In how many days can A alone finish the job?
- A. 20
- B. 30
- C. 60
- D. 15
Show answer and solution
Answer: (B) 30
Take the job as 60 units (LCM of 10, 12, 20).
A + B = 6 units/day, B + C = 5 units/day, C + A = 3 units/day.
Adding: 2(A + B + C) = 14 ⇒ A + B + C = 7 units/day.
A = 7 − (B + C) = 7 − 5 = 2 units/day, so A alone needs 60/2 = 30 days. (B = 4 units/day → 15 days; C = 1 unit/day → 60 days.)
Tip: Choosing total work = LCM of the given times avoids fractions entirely.
A + B = 6 units/day, B + C = 5 units/day, C + A = 3 units/day.
Adding: 2(A + B + C) = 14 ⇒ A + B + C = 7 units/day.
A = 7 − (B + C) = 7 − 5 = 2 units/day, so A alone needs 60/2 = 30 days. (B = 4 units/day → 15 days; C = 1 unit/day → 60 days.)
Tip: Choosing total work = LCM of the given times avoids fractions entirely.
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