Question : 4 men and 6 women can complete a task in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
Option 1: 44
Option 2: 40
Option 3: 15
Option 4: 16
Correct Answer: 40
Solution :
Given: $4$ men ($M$) and $6$ women ($W$) can complete a task in $8$ days.
$3$ men and $7$ women can complete it in $10$ days.
According to the question,
$(4M + 6W)×8 = (3M + 7W)×10$
$⇒32M + 48W = 30M + 70W$
$⇒2M = 22W$
$⇒M=11W$
Now, $4M + 6W = 4\times 11W + 6W = 50W$.
Therefore, 50 women can do the work in 8 days.
So, the time taken by 10 women to complete the work =$\frac{50\times 8}{10}=40$ days
Hence, the correct answer is 40.
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