What is the length of the platform?

Question

A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds.
What is the length of the platform?

Answer 1

The platform is 400 meters long.
Let the length of first Train be T. So, the length of the second train is 0.5T. Let the length of the platform be P.
The first train has to travel a distance of 1.5T in order to cross the oncoming train. The effective speed is 48 + 42 KMPH = 90 KMPH = 90,000/3,600 = 25 meters per sec. If it travels 1.5 T meters in 12 seconds at 25 meters per second, T = 12*25/1.5 = 200 meters.

In order to cross the platform fully, the train has to travel a distance of T+P meters. If that is accomplished in 45 seconds at the speed of 48 KMPH, (T+P)/45 = 48,000/3600. T+P = 48,000*45/3,600 = 600. As T= 200, P = 600-200 = 400 m.

Answer 2

Length of the platform is 400 meter.