Question
Efficiency of a man is 25% more than that of a woman.
(n - 10) men working 6 hours a day can complete a task in 18 days, whereas (n - 9) women working 6 hours a day can complete the same task in 20 days. Find the time taken by (n + 2) men and (n - 3) 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; (n - 10) × 6 × 18 × 5e = (n - 9) × 6 × 20 × 4e Or, 540n - 5400 = 480n - 4320 Or, 60n = 1080 Or, 'n' = 18 Total work = (n - 10) × 6 × 18 × 5e = 8 × 6 × 18 × 5e = '4320e' units So, required number of days to complete the work = 4320e ÷ [(20 × 5e + 15 × 4e) × 9] = 4320e ÷ (160e × 9) = 4320e ÷ 1440e = 3 days
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