25 men with 10 boys can do in 6 days as much work as 21 men with 30 boys can do in days. How many boys must help 40 men to do the same work in 4 days ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let 1 men's 1 day's work}} = x \cr & {\text{and 1 boy's 1 day's work}} = y \cr & {\text{Then, }} \cr & \Rightarrow {\text{6}}\left( {25x + 10y} \right) = 5\left( {21x + 30y} \right) \cr & \Rightarrow 150x + 60y = 105x + 150y \cr & \Rightarrow 45x = 90y \cr & \Rightarrow x = 2y \cr & {\text{Let,}} \cr & {\text{The required number of boys be }}z \cr & {\text{Then,}} \cr & \Rightarrow {\text{4}}\left( {40x + zy} \right) = 6\left( {25x + 10y} \right) \cr & \Rightarrow 4\left( {80y + zy} \right) = 6\left( {50y + 10y} \right) \cr & \Rightarrow 80 + z = \frac{{6 \times 60}}{4} = 90 \cr & \Rightarrow z = 10 \cr} $$