Five men and 2 boys can do in 30 days as much work as 7 men and 10 boys can do in 15 days. How many boys should join 40 men to do the same work in 4 days?

10

5M + 2B = 30 days

150M + 60B            ..(1)       (Multiplied by 30 to get it done in 1 day)

7M + 10B = 15 days

105M + 150B          ..(2)        (Multiplied by 15 to get it done in 1 day)

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

⇒ 45M = 90B

⇒ M : B = 90 : 45 = 2 : 1 (Efficiencies)

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

⇒ [150 (2) + 60(1)] = 360 units.

 Hence, no. of boys that should join 40 men to do the same work in 4 days

⇒ \(\frac{360}{40(2) + x}\) = 4

⇒ 360 = 320 + 4x

⇒ 4x = 40

⇒ x =10 

Therefore, 10 boys are needed with 40 men to complete the same work in 4 days.