Question : 8 men can complete a task in 45 days. 8 women can complete the same task in 18 days. In how many days will 5 men and 8 women, together, complete the same task?
Option 1: $13 \frac{1}{5}$
Option 2: $12 \frac{4}{5}$
Option 3: $14 \frac{2}{5}$
Option 4: $15 \frac{3}{5}$
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Correct Answer: $14 \frac{2}{5}$
Solution : First, use $M_1D_1= M_2D_2$ Where $M_1$ and $M_2$ are men and women and $D1$ and $D_2$ are days. $8M\times 45 = 8 W\times 18$ ⇒ $5M=2W$ So, $5M + 8W=2W + 8W = 10W$ Now, $8\times 18 = 10\times D_3$ ⇒ $D_3 = \frac{8\times 18}{10} =\frac{72}{5}=14 \frac{2}{5}$ days. Hence, the correct answer is $14 \frac{2}{5}$.
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