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

Speed of the first train = 48 km/hr.
Let the length of the first train = 2x meter.
Speed of the second train = 42 km/hr.
Let the length of the second train = x meter.
Distance = (2x + x) = 3x meter.
Time = 12 seconds
Relative speed = 48 + 42 = 90 km/hr.
= 90 × (5/18) = 25 m/s.
3x = 25 × 12
⇒ x = 100 meter.
Length of the first train = 200
Time is taken to cross the platform = 45 seconds.
Speed of first train = 48 km/hr
= 48 × (5/18)
= 40/3 m/s.
Let the length of the platform = y meter.
Distance = 200 + y meter.
⇒ 200 + y = 45 × (40/3)
⇒ 200 + y = 600
⇒ y = 400 meter.