A train covers a distance between two stations A and B in 45 minutes. If the speed of the train is reduced by 5 km/hr, then it covers the distance in 48 minutes. The distance between the stations A and B is :

Solution(By Examveda Team)

Let the distance between the stations A and B br x km
Time taken = 45 min = $$\frac{3}{4}$$ hrs
∴ Original speed :
$$\eqalign{ & = \left( {x \times \frac{4}{3}} \right){\text{km/hr}} \cr & {\text{ = }}\frac{{4x}}{3}{\text{km/hr}} \cr} $$
New speed :
$$\eqalign{ & = \left( {\frac{{4x}}{3} - 5} \right){\text{km/hr}} \cr & = \left( {\frac{{4x - 15}}{3}} \right){\text{km/hr}} \cr & \therefore \frac{x}{{\left( {\frac{{4x - 15}}{3}} \right)}} = \frac{{48}}{{60}} \cr & \Rightarrow \frac{{3x}}{{4x - 15}} = \frac{4}{5} \cr & \Rightarrow 15x = 16x - 60 \cr & \Rightarrow x = 60\text{ km} \cr} $$