Question
Efficiency of a man is 25% more than that of a woman.
(n + 4) men working 8 hours a day can complete a task in 20 days, whereas (2n - 4) women working 6 hours a day can complete the same task in 25 days. Find the time taken by (n - 2) men and (n - 4) 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 + 4) × 8 × 20 × 5e = (2n - 4) × 6 × 25 × 4e Or, 800n + 3200 = 1200n - 2400 Or, 5600 = 400n Or, 'n' = 14 Total work = (n + 4) × 8 × 20 × 5e = 18 × 8 × 20 × 5e = '14400e' units So, required number of days to complete the work = 14400e ÷ [(12 × 5e + 10 × 4e) × 9] = 14400e ÷ (100e × 9) = 14400e ÷ 900e = 16 days
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