A train passes a station platform in 36 seconds and a man standing on the platform in 52/3 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

Question: A train passes a station platform in 36 seconds and a man standing on the platform in 52/3 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

Solution:
Speed = 54 km/hr = (54 × 1000)/3600 m/s
= 15 m/s

Length of the train = 15 × (52/3) m = 260 m.

Let,
The length of the platform be x meters
∴ (260 + x)/36 = 15
⇒ 260 + x = 540
⇒ x = 540 - 260
∴ x = 280

∴ The length of the platform 280 meters