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    Question

    A and B can complete a piece of work in 12 days, B and C

    in 15 days and A and C in 20 days. In how many days can B alone complete the work?
    A 20 days Correct Answer Incorrect Answer
    B 10 days Correct Answer Incorrect Answer
    C 18 days Correct Answer Incorrect Answer
    D 27 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Let rates be a, b, c. a + b = 1/12 b + c = 1/15 a + c = 1/20 Add: 2(a + b + c) = 1/12 + 1/15 + 1/20 = (5 + 4 + 3)/60 = 12/60 = 1/5 ⇒ a + b + c = 1/10 b = (a + b + c) − (a + c) = 1/10 − 1/20 = 1/20 So B alone takes 20 days.

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