Question : 3 men or 5 women can do a work in 57 days. In how many days can 9 men and 4 women do that same work?
Option 1: 16 days
Option 2: 18 days
Option 3: 14 days
Option 4: 15 days
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Correct Answer: 15 days
Solution :
According to the question,
3 men = 5 women
1 man = $\frac{5}{3}$ women
9 men = $9 \times \frac{5}{3}$ women = 15 women
Now the total work is done by = 15 women and 4 women = 19 women
Let the total work be completed by 19 women in $x$ days.
We know that 5 women can complete the work in 57 days.
$M_1D_1= M_2D_2$
Where $M_1$ and $M_2$ are women and $D1$ and $D_2$ are days.
$⇒5 \times 57= 19 \times x$
$⇒x = \frac{5 \times 57}{19} = 15$ days.
Hence, the correct answer is 15 days.
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