Question
A and B together can complete a piece of work in 12 days. B and C together can complete the same work in 15 days, and A and C together can complete it in 20 days. In how many days can all three together complete the work?
Solution
Let total work = W units. (A + B)’s rate = W/12 (B + C)’s rate = W/15 (A + C)’s rate = W/20 Add all three equations: (A + B) + (B + C) + (A + C) = 2(A + B + C) So, 2(A + B + C) rate = W/12 + W/15 + W/20 Take LCM = 60: = (5W + 4W + 3W) / 60 = 12W / 60 = W/5 So 2(A + B + C) rate = W/5 ⇒ (A + B + C) rate = (W/5) / 2 = W/10 Time taken by A, B and C together = W / (W/10) = 10 days
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