If 4 men and 6 boys can do a work in 8 days and 6 men and 4 boys can do the same work in 7 days, then how many days will 5 men and 4 boys take to do the same work?

8

4M + 6B = 8 days

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

6M + 4B = 7 days

42M + 28B          ..(2)    (Multiplied by 7 to get it in 1 day)

⇒ NOW, (1) - (2), WE GET 

⇒ 10M = 20B

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

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

⇒ 32(2) + 48(1) ⇒ 112 units.

now the time it would take 5 men and 4 boys to complete the work is =

⇒ \(\frac{112}{5(2)+ 4(1)}\) = \(\frac{112}{14}\) = 8 days.