How to solve ?

Suppose they normally reach the crossing together at 9:30
Today the cyclist will reach at 9:55, so @ 10 km/hr, (s)he will be 5 km away at 9:25.
The train still reaches at 9:30, so it covers 5 km in 5 mins
Thus speed of train = 1 km/min = 60 km/h <-----

Every day a cyclist meets a train at a particular crossing.
The road is straight before the crossing and both are traveling in the same direction.
The cyclist travels with a speed of 10 Kmph.
One day the cyclist comes late by 25 min. and meets the train 5 km before the crossing.
What is the speed of the train?
Cyclist and Train meet at 5 km point.
If cyclist had left on time, they would be 25 min at 10 km/h further 10 km/h * 25/60 h = 25/6 km
This leaves the cyclist 5/6 km from the cross road, when the train is at 5 km
Time cyclist takes to travel this 5/6 km = distance / speed
(5/6) / 10 = 1 / 12 hours
The train travels 5 km in 1/12 h
Speed = distance / time
5 / (1/12) = 5 * 12 = 60 km / h