A train of 450 meters long moving with a speed of 65 km/hr crosses a man travelling in some direction of the train in 27 seconds. Then the speed with which the man moving and his direction is

Given:

Length of train = 450 m

Speed of train = 65 km/hr

Time taken to cross man = 27 sec

Formula used:

Relative Speed = \(\frac{\text{Distance}}{\text{Time}}\)

If moving in same direction: Relative speed = Train speed − Man speed

If opposite direction: Relative speed = Train speed + Man speed

Calculations:

Relative speed = \(\frac{450}{27} \times \frac{18}{5} = 60\) kmph

Let man's speed be x kmph

If same direction: \(65 - x = 60\)

⇒ \(x = 65 - 60 = 5\) kmph

If the opposite direction: \(65 + x = 60\)

⇒ \(x = 60 - 65 = -5\) kmph

Negative speed is not possible. So, the man is moving in the same direction as the train at 5 km/hr.

∴ The correct answer is Option (3).