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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