Question
Efficiency of a man is 50% more than that of a woman. (n - 10) men working 6 hours a day can complete a task in 15 days, whereas (n - 9) women working 6 hours a day can complete the same task in 20 days. Find the time taken by (n - 4) men and (n - 3) women working 10 hours a day to complete the task.
Solution
Let the efficiency of a woman be '2e' units/day. Then, efficiency of a man = (3/2) × 2e = '3e' units/day. ATQ; (n - 10) × 6 × 15 × 3e = (n - 9) × 6 × 20 × 2e Or, 270n - 2700 = 240n - 2160 Or, 30n = 540 Or, 'n' = 18 Total work = (n - 10) × 6 × 15 × 3e = 8 × 6 × 15 × 3e = '2160e' units So, required number of days to complete the work = 2160e ÷ [(14 × 3e + 15 × 2e) × 10] = 2160e ÷ (72e × 10) = 2160e ÷ 720e = 3 days
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