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?
Answer & explanation
Correct answer: option 1
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.