Single correct option
A and B together can finish a job in 15 days, B and C together in 20 days, and C and A together in 12 days. In how many days can A alone finish the job?
- A. 15
- B. 20
- C. 24
- D. 30
Show answer and solution
Answer: (B) 20
Daily rates: A + B = 1/15, B + C = 1/20, C + A = 1/12.
Adding all three: 2(A + B + C) = 1/15 + 1/20 + 1/12 = (4 + 3 + 5)/60 = 12/60 = 1/5, so A + B + C = 1/10.
A = (A + B + C) − (B + C) = 1/10 − 1/20 = 1/20.
So A alone needs 20 days. Likewise B = 1/12 − 1/10 ... using A+B=1/15 gives B=1/15-1/20=1/60 (60 days) and C = 1/10-1/20=1/20 (20 days, matching C+A check).
Tip: With three pairwise rates, add them and halve to get the combined rate. Then subtract a pair to get the single rate.
Adding all three: 2(A + B + C) = 1/15 + 1/20 + 1/12 = (4 + 3 + 5)/60 = 12/60 = 1/5, so A + B + C = 1/10.
A = (A + B + C) − (B + C) = 1/10 − 1/20 = 1/20.
So A alone needs 20 days. Likewise B = 1/12 − 1/10 ... using A+B=1/15 gives B=1/15-1/20=1/60 (60 days) and C = 1/10-1/20=1/20 (20 days, matching C+A check).
Tip: With three pairwise rates, add them and halve to get the combined rate. Then subtract a pair to get the single rate.
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