4 men and 7 women can do a work in 8 days, 7 men and 4 women can do the same work in 5 days. Find the number of days in which 8 women can find the work.

55 Days

4M + 7W = 8 days,

32M + 56W         ..(1)       (Multiplied by 8 to get it done in 1 day)

7M + 4W = 5 days,

35M + 20W         ..(2)       (Multiplied by 5 to get it done in 1 day)

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

⇒ 3M = 36W

⇒ M : W = 36 : 3 = 12 : 1 (Efficiencies)

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

⇒ [32 (12) + 56(1)] = 440 units.

Hence, time taken by 8 women to complete total work is = \(\frac{440}{8(1)}\) = 55 days.         ..(\(\frac{Work}{Efficiency}\) = Time)