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.
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) × 8 × 18 × 5e = (3n - 2) × 6 × 24 × 4e Or, 1440n + 2880 = 1728n - 576 Or, 2880 + 576 = 1728n - 1440n Or, 3456 = 288n Or, 'n' = 12 Total work = (2n + 4) × 8 × 18 × 5e = (28) × 8 × 18 × 5e = '20160e' units So, required number of days to complete the work = 20160e ÷ [(6 × 5e + 4 × 4e) × 9] = 20160e ÷ (46e × 9) = 20160e ÷ 414e = 40 days
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