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    Question

    A, B, and C can complete a task individually in 45, 35,

    and 63 days respectively. They start working together, but A leaves 24 days before the work is completed, and B leaves 10 days after A leaves. How many total days does it take to finish the work?
    A 25 days Correct Answer Incorrect Answer
    B 27 days Correct Answer Incorrect Answer
    C 29 days Correct Answer Incorrect Answer
    D 31 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let total amount of work = 315 units (LCM of 45, 35 and 63)

    Amount of work done by A in one day = 315/45 = 7 units

    Amount of work done by B in one day = 315/35 = 9 units

    Amount of work done by C in one day = 315/63 = 5 units

    Let total time taken to complete the whole work is ‘x’ days

    According to question;

    5 × x + 9 × (x – 14) + 7 × (x – 24) = 315

    Or, 21x = 315 + 168 + 126

    Or, 21x = 609

    Or, x = 29

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