Question : 12 men and 12 women can complete a piece of work in 9 days. 6 men and 15 women can complete the same work in 12 days. How long (in days) would it take 9 women to complete half the work?
Option 1: 36
Option 2: 12
Option 3: 18
Option 4: 24
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Correct Answer: 18
Solution : Let M be the efficiency of a man and W be the efficiency of a woman. Total work = (12M + 12W) × 9 ------------(1) Total work = (6M + 15W) × 12 ------------(2) From (1) and (2), ⇒ (12M + 12W) × 9 = (6M + 15W) × 12 ⇒ 108M + 108W = 72M + 180W ⇒ 36M = 72W ⇒ M : W = 2 : 1 Let the total work = (6M + 15W) × 12 = (6 × 2 + 15) × 12 = (12 + 15) × 12 = 324 units So, the time taken by 9 women to complete half of the work = $\frac{324}{2}×\frac{1}{9}$ = 18 days Hence, the correct answer is 18.
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