If a train takes 1.5 sec to cross a telegraph post and 1.75 to overtake a cyclist racing along the parallel road to the track at 10 m/s , then the length of the train is:

Let the length of the train be x metres and its speed be y m/sec.
Then,
x/y = 1.75
⇒ x = 1.75y

Since the train takes less time to pass a moving object than a stationary object,
it means that the cyclist is moving in a direction opposite to that of the train.

∴ x/(y + 10) = 1.5
⇒ x = 1.5 y + 15
⇒ 1.75 y = 1.5 y + 15
⇒ 0.25 y = 15
⇒ y = 15/0.25
⇒ y = 60.

Length of the train = 1.75 y = (1.75 × 60) m
= 105 m.