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
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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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