With an average speed of 50 km/hr, a train reaches its destination in time. If it goes with an average speed of 40 km/hr, it is late by 24 min. The total journey is :

Difference between timings = 24 min = $$\frac{24}{60}$$ hr = $$\frac{2}{5}$$ hr
Let the length of the journey be x km
Then,
$$\eqalign{ & \Leftrightarrow \frac{x}{{40}} - \frac{x}{{50}} = \frac{2}{5} \cr & \Leftrightarrow \frac{x}{{200}} = \frac{2}{5} \cr & \Leftrightarrow x = \left( {\frac{2}{5} \times 200} \right) \cr & \Leftrightarrow x = 80{\text{ km}} \cr} $$