Two men and 7 women can complete a work in 28 days whereas 6 men and 16 women can do the same work in 11 days. In how many days can 7 men complete the same work?

22

2M + 7W = 28 days

56M + 196W    ..(1)       (Multiplied by 28 to get it done in 1 day)

6M + 16W = 11 days

66M + 176W   ..(2)        (Multiplied by 11 to get it done in 1 day)

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

⇒ 10M = 20W

⇒ M : W = 20 : 10 = 2 : 1 (Efficiencies)

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

⇒ [56 (2) + 196(1)] = 308 units.

⇒ Time required for 7 men to complete the total work = \(\frac{308}{7(2)}\) = \(\frac{308}{14)}\) = 22 days