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    Question

    'A' can complete a task in 24 days, while 'B' can finish

    the same task in 36 days. However, 'A' works at only 2/3 of his usual efficiency, and 'B' operates at 50% of his normal efficiency. Given these conditions, determine the number of days required for both of them, working together, to complete 75% of the task.
    A 18 days Correct Answer Incorrect Answer
    B 24 days Correct Answer Incorrect Answer
    C 15 days Correct Answer Incorrect Answer
    D 12 days Correct Answer Incorrect Answer

    Solution

    Let the total work be 72 units (LCM of 24 and 36) .

    Efficiency of 'A' = (72/24) = 3 units/day

    Efficiency of 'B' = (72/36) = 2 units/day

    New efficiency of 'A' = (2/3) X 3 = 2 units/day

    New efficiency of 'B' = 0.5 X 2 = 1 unit/day

    Therefore, required time taken = (0.75 X 72) ÷ (2 + 1) = (54/3) = 18 days

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