A train travelling at 48 km/h completely crosses an another train having half length of first train and travelling in opposite directions at 42 km/h in 12 s. It also passes a railways platform in 45 s . The length of the platform is?

Let the length of the first train be x m.
Then, the length of second train is (x/2) m
∴ Relative speed = (48 + 42) km/h = (90 x 5/18) m/s = 25 m/s
According to the question. (x + x/2) / 25 = 12
⇒ 3x/2 = 300
⇒ x = 200 m
∴ Length of first train = 200 m
Let the length of platform be y m .
Speed of the first train = (48 x 5/18) m/s = 40/3 m/s
Time = Distance / Speed
∴ (200 + y) x 3/40 = 45
⇒ 600 + 3y = 1800
∴ y = 400 m