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    Question

    Worker 'A' can complete the entire task alone in 12.5

    days, while worker 'B' can finish it in 25 days. If they take turns working on the task each day, with 'B' starting on the first day, how many days will it take for them to complete the work together?
    A 15 days Correct Answer Incorrect Answer
    B 17 days Correct Answer Incorrect Answer
    C 17.5 days Correct Answer Incorrect Answer
    D 16.5 days Correct Answer Incorrect Answer

    Solution

    Let the total work be 25 units (LCM of 12.5 and 25)
    Efficiency of 'A' = (25/12.5) = 2 units/day
    Efficiency of 'B' = (25/25) = 1 unit/day
    Work done by them in first 2 days = 1 + 2 = 3 units
    Work done by them in first 16 days = 3 X 8 = 24 units
    Remaining work = 25 - 24 = 1 unit
    Time taken by 'B' to complete remaining work = (1/1) = 1 day
    Therefore, required time = 16 + 1 = 17 days

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