Question

    A, B, and C can complete a piece of work in 30 days, 40

    days, and 60 days respectively. If all of them started working together and after 12 days A left the work, and B left the work 6 days after A left the work, then the whole work will be completed in how many days?
    A 30 days Correct Answer Incorrect Answer
    B 12 days Correct Answer Incorrect Answer
    C 27 days Correct Answer Incorrect Answer
    D 25 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Let total work = 120 units (LCM of 30, 40, and 60) Efficiency of A = 120/30 = 4 units per day Efficiency of B = 120/40 = 3 units per day Efficiency of C = 120/60 = 2 units per day Amount of work done by A, B, and C in 12 days = 12 × (4 + 3 + 2) = 12 × 9 = 108 units Amount of work done by B and C together in 6 days = 6 × (3 + 2) = 6 × 5 = 30 units Remaining work = 120 – 108 – 30 = 18 units Time taken by C to complete 18 units of work = 18/2 = 9 days Desired time = 12 + 6 + 9 = 27 days

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