Question
Efficiency of a man is 20% 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 8 hours a day can complete the same task in 12 days. Find the time taken by (n - 3) men and (n - 4) women working 9 hours a day to complete the task.
Solution
Let the efficiency of a woman be '5e' units/day. Then, efficiency of a man = (6/5) × 5e = '6e' units/day. ATQ; (n - 10) × 6 × 15 × 6e = (n - 9) × 8 × 12 × 5e Or, 540n - 5400 = 480n - 4320 Or, 60n = 1080 Or, 'n' = 18 Total work = (n - 10) × 6 × 15 × 6e = 8 × 6 × 15 × 6e = '4320e' units So, required number of days to complete the work = 4320e ÷ [(15 × 6e + 14 × 5e) × 9] = 4320e ÷ (160e × 9) = 4320e ÷ 1440e = 3 days
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