Question : 3 men and 5 women together can complete a work in 6 days, whereas 4 men and 9 women together can do it in 4 days. How many women are required to do the same work in 7 days?
Option 1: 15
Option 2: 12
Option 3: 14
Option 4: 10
Correct Answer: 12
Solution :
Given: 3 men and 5 women together can complete a work in 6 days, whereas 4 men and 9 women together can do it in 4 days.
Let the efficiency of 1 man and 1 woman be $x$ and $y$.
According to the question,
$(3x + 5y)6 = (4x + 9y)4$
⇒ $18x + 30y = 16x + 36y$
⇒ $18x - 16x = 36 - 30y$
⇒ $2x = 6y$
⇒ $\frac{x}{y} = \frac{6}{2} = \frac{3}{1}$
⇒ $x : y = 3 : 1$
Let the total work $=(3 \times 3 + 5 \times 1)×6 = 84$
Let $n$ women complete the whole work in 7 days with the efficiency of 1,
⇒ $n \times 1 \times 7 = 84$
⇒ $n = \frac{84}{7} = 12$
Hence, the correct answer is 12.
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