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    Question

    Efficiency of a man is 25% more than that of a woman.

    (2n + 4) men working 6 hours a day can complete a task in 15 days, whereas (3n - 2) women working 5 hours a day can complete the same task in 18 days. Find the time taken by (n - 4) men and (n - 4) women working 8 hours a day to complete the task.
    A 14 days Correct Answer Incorrect Answer
    B 16 days Correct Answer Incorrect Answer
    C 20 days Correct Answer Incorrect Answer
    D 30 days Correct Answer Incorrect Answer
    E 24 days Correct Answer Incorrect Answer

    Solution

    Let the efficiency of a woman be '4e' units/day.
    Then, efficiency of a man = (5/4) × 4e = '5e' units/day.

    ATQ;

    (2n + 4) × 6 × 15 × 5e = (3n - 2) × 5 × 18 × 4e

    Or, (2n + 4) × 450e = (3n - 2) × 360e

    Or, 900n + 1800 = 1080n - 720

    Or, 1800 + 720 = 1080n - 900n

    Or, 2520 = 180n

    Or, 'n' = 14

    Total work = (2n + 4) × 6 × 15 × 5e = (2 × 14 + 4) × 6 × 15 × 5e = 32 × 6 × 15 × 5e = '14400e' units

    So, required number of days to complete the work = 14400e ÷ [(10 × 5e + 10 × 4e) × 8] = 14400e ÷ (90e × 8) = 14400e ÷ 720e = 20 days 

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