2 men and 7 women can complete a work in 28 days, where as 6 men and 16 women can do the same work in 11 days. In how many days will 5 men and 4 women, working together, complete the same work? 

22

Men = M           Women = W

(2M + 7W) × 28 = (6M + 16W)11

56M + 196W = 66M + 176W

20W = 10M   

2W = 1M  (or Efficiency of M : W = 2 : 1)                                            

Now → 2 M + 7 W ⇒ 28 days                       

             ↓ x2 (Changing in women)             

          4 W + 7 W ⇒ 28 days

                  11 W ⇒ 28 days 

Total work = efficiency × time =  11 W × 28 days = 308

We have

⇒ 5M + 4W    

    ↓ x2 (changing in women)

⇒ 10 W + 4 W = 14 W

14W or (5M + 4W) can do it in = \(\frac{308}{14}\) = 22 days