Question : 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 25 women complete it?
Option 1: 20
Option 2: 16
Option 3: 25
Option 4: 18
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Correct Answer: 16
Solution :
Given:
4 men and 6 women can complete a task in 8 days.
3 men and 7 women can complete the same task in 10 days.
We know, $M_1D_1= M_2D_2$
Where $M_1$ and $M_2$ are men + women and $D1$ and $D_2$ are days.
So, (4M + 6W) × 8 = (3M + 7W) × 10
⇒ 32M + 48W = 30M + 70W
⇒ 2M = 22W
⇒ 1M = 11W
⇒ 4M = 11 × 4 W = 44W
4 Men + 6 women = 44 women + 6 women = 50 women
So, 50 women can do the task in 8 days.
$\therefore$ 25 women can do that same task in $\frac{50×8}{25}=16$ days
Hence, the correct answer is 16.
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