A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is :

Solution(By Examveda Team)

Let distance = x km and usual rate = y kmph
$$\eqalign{ & \Rightarrow \frac{x}{y} - \frac{x}{{y + 3}} = \frac{{40}}{{60}} \cr & \Rightarrow 2y\left( {y + 3} \right) = 9x.....(i) \cr} $$
And,
$$\eqalign{ & \Rightarrow \frac{x}{{y - 2}} - \frac{x}{y} = \frac{{40}}{{60}} \cr & \Rightarrow y\left( {y - 2} \right) = 3x.....(ii) \cr} $$
On dividing (i) by (ii), we get :
$$\eqalign{ & \Rightarrow 2\left( {y + 3} \right) = 3\left( {y - 2} \right) \cr & \Rightarrow y = 12 \cr} $$
∴ Distance :
$$\eqalign{ & = x{\text{ km}} \cr & = \left( {\frac{{2y\left( {y + 3} \right)}}{9}} \right){\text{ km}} \cr & = \left( {\frac{{2 \times 12 \times 15}}{9}} \right){\text{ km}} \cr & = 40{\text{ km}} \cr} $$