3 men and 7 women can complete a task in 10 days. On the other hand, 4 men and 6 women, take 8 days to complete the same task. How long will it take 10 women to complete the same task?

40 days

3M + 7W = 10 days,

30M + 70W       ..(1)       (Multiplied by 10 to get it done in 1 day)

4M + 6W = 8 days,

32M + 48W       ..(2)        (Multiplied by 8 to get it done in 1 day)

Now, (1) - (2), we get

⇒ 2M = 22W

⇒ M : W = 22 : 2 = 11 : 1  (Efficiencies)

Putting efficiency in equation (1), and we get the total work 

⇒ [30 (11) + 70 (1)] = 400 units.

⇒ Time required by 10 Women to complete the work = \(\frac{400}{10(1)}\) = 40 days,     ..(\(\frac{Work}{Efficiency}\) = Time)