Discussion
Two men and 7 women can complete a work in 28 days, whereas 6 men and 16 women can do the same work in 11 days. In how many days will 5 men and 4 women, working together, complete the same work ?
Answer: D
They will take 22 days.
Equate the total work in the two cases:
\[ \begin{aligned} 28(2m + 7w) &= 11(6m + 16w) \\ 56m + 196w &= 66m + 176w \\ 10m = 20w &\Rightarrow m = 2w \end{aligned} \]
So the work is \(28(4w + 7w) = 308\) woman-days, and 5 men and 4 women equal 14 women: \(\frac{308}{14} = 22\) days.
Check: 2 men and 7 women equal 11 women, and \(11 \times 28 = 308\); 6 men and 16 women equal 28 women, and \(28 \times 11 = 308\).
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