A train travelling at 36 kmph completely crosses another train having half its length and travelling in the opposite direction at 54 kmph, in 12 second, If it also passes a railway platform in 1 1/ 2 minutes, the length of the platform is?

Let the length of slower train be L meters and the
length of faster train be (L/2) meters
Their relative speed = (36 + 54) km/hr
= 90 x (5/18)
= 25 m/sec
∵ 3L / (2 x 25) = 12
⇒ 3L = 600
⇒ L = 200
∴ Length of slower train = 200 meters
Let the length of platform by M meters
Then, 200 + M/[36 x (5/18)] = 90 sec.
⇒ 200 + M = 900
⇒ M = 700 meters
Length of platform = 700 meters.