Single correct option
A and B together can finish a job in 12 days, B and C together in 15 days, and C and A together in 20 days. In how many days can A alone finish the job?
- A. 24
- B. 30
- C. 36
- D. 40
Show answer and solution
Answer: (B) 30
Adding the three pair rates counts each person twice:
2(A + B + C) = 1/12 + 1/15 + 1/20 = (5 + 4 + 3)/60 = 1/5.
So A + B + C = 1/10 per day.
A = (A + B + C) − (B + C) = 1/10 − 1/15 = 1/30.
A alone takes 30 days.
Tip: take the total work as the LCM (60 units). The pair rates are 5, 4 and 3 units/day, so the sum of all three is 6 and A = 6 − 4 = 2 units/day, giving 30 days.
2(A + B + C) = 1/12 + 1/15 + 1/20 = (5 + 4 + 3)/60 = 1/5.
So A + B + C = 1/10 per day.
A = (A + B + C) − (B + C) = 1/10 − 1/15 = 1/30.
A alone takes 30 days.
Tip: take the total work as the LCM (60 units). The pair rates are 5, 4 and 3 units/day, so the sum of all three is 6 and A = 6 − 4 = 2 units/day, giving 30 days.
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