Question
A and B together can complete a piece of work in 8 days.
B and C together can also complete it in 8 days, while A and C together can complete it in 6 days. In how many days can B alone complete the work?Solution
Let the work done per day by A, B, C be a, b, c respectively. A + B = 1/8 …(i) B + C = 1/8 …(ii) A + C = 1/6 …(iii) Add (i), (ii), (iii): (A + B) + (B + C) + (A + C) = 1/8 + 1/8 + 1/6 2(A + B + C) = 1/4 + 1/6 1/4 + 1/6 = (3/12 + 2/12) = 5/12 So 2(A + B + C) = 5/12 ⇒ A + B + C = 5/24 Now b = (A + B + C) − (A + C) = 5/24 − 1/6 1/6 = 4/24 So b = 5/24 − 4/24 = 1/24 Therefore B alone takes 24 days to complete the work.
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