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    Question

    A and B can together complete a work in 8 days, B and C

    in 12 days, and C and A in 16 days. In how many days can C alone complete the work?
    A 32 days Correct Answer Incorrect Answer
    B 96 days Correct Answer Incorrect Answer
    C 77 days Correct Answer Incorrect Answer
    D 68 days Correct Answer Incorrect Answer

    Solution

    ATQ, Let daily work rates of A, B, C be a, b, c. a + b = 1/8 b + c = 1/12 c + a = 1/16 Add all: 2(a + b + c) = 1/8 + 1/12 + 1/16 LCM(8,12,16) = 48 1/8 = 6/48, 1/12 = 4/48, 1/16 = 3/48 Sum = 13/48 β‡’ a + b + c = 13/96 Now: a = (a + b + c) βˆ’ (b + c) = 13/96 βˆ’ 1/12 1/12 = 8/96 β‡’ a = (13 βˆ’ 8)/96 = 5/96 β‡’ A alone: 96/5 = 19.2 days b = (a + b + c) βˆ’ (c + a) = 13/96 βˆ’ 1/16 1/16 = 6/96 β‡’ b = (13 βˆ’ 6)/96 = 7/96 β‡’ B alone: 96/7 days c = (a + b + c) βˆ’ (a + b) = 13/96 βˆ’ 1/8 1/8 = 12/96 β‡’ c = (13 βˆ’ 12)/96 = 1/96 β‡’ C alone: 96 days. Hence, C alone can complete work in 96 days

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