A train starts from station A and reaches B 15 minutes late when it moves with 40 km/hr and 24 minutes late when it goes 30 km/hr. The distance between the two stations is

Let the distance between the two stations be $$d$$ km and time taken be $$t$$ hours.

When it moves with 40 km/hr, it reaches 15 mins late, so total time taken is

=> $$\frac{d}{40} = t + \frac{15}{60}$$ --------Eqn(1)

Similarly,

=> $$\frac{d}{30} = t + \frac{24}{60}$$ -----------Eqn(2)

Subtracting eqn(1) from (2), we get :

=> $$\frac{d}{30}-\frac{d}{40} = \frac{9}{60}$$

=> $$\frac{d}{120} = \frac{9}{60}$$

=> $$d$$ = 9*2 = 18 km