A project can be completed by 2 men and 5 women in 8 days while 4 men and 6 women can complete the same project in 5 days. How many men will be required to complete this project in 4 days?

8

2M + 5W = 8 days,

16M + 40W     ..(1)       (Multiplied by 8 to get it done in 1 day)

4M + 6W = 5 days,

20M + 30W     ..(2)        (Multiplied by 5 to get it done in 1 day)

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

⇒ 4M = 10W

⇒ M : W = 10 : 4 = 5 : 2  (Efficiencies)

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

⇒ [16 (5) + 40 (2)] = 160 units.

⇒ No. of men needed to complete total work in 4 days = \(\frac{160}{M(5)}\) = 4 days 

⇒ 5M = 40

⇒ M = 8,

Therefore 8 men are needed to complete the work in 4 days.