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    Question

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

    (2n + 4) men working 8 hours a day can complete a task in 18 days, whereas (3n - 2) women working 6 hours a day can complete the same task in 24 days. Find the time taken by (n - 6) men and (n - 8) women working 9 hours a day to complete the task.
    A 24 days Correct Answer Incorrect Answer
    B 30 days Correct Answer Incorrect Answer
    C 32 days Correct Answer Incorrect Answer
    D 36 days Correct Answer Incorrect Answer
    E 40 days Correct Answer Incorrect Answer

    Solution

    Let the efficiency of a woman be '4e' units/day. Then, efficiency of a man = (5/4) ├Ч 4e = '5e' units/day. ATQ; (2n + 4) ├Ч 8 ├Ч 18 ├Ч 5e = (3n - 2) ├Ч 6 ├Ч 24 ├Ч 4e Or, 1440n + 2880 = 1728n - 576 Or, 2880 + 576 = 1728n - 1440n Or, 3456 = 288n Or, 'n' = 12 Total work = (2n + 4) ├Ч 8 ├Ч 18 ├Ч 5e = (28) ├Ч 8 ├Ч 18 ├Ч 5e = '20160e' units So, required number of days to complete the work = 20160e ├╖ [(6 ├Ч 5e + 4 ├Ч 4e) ├Ч 9] = 20160e ├╖ (46e ├Ч 9) = 20160e ├╖ 414e = 40 days

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