Train M crosses a platform in 60 seconds and overtakes a man running in the opposite direction at 12 km/h in 30 seconds. Train N passes Train M, which is moving in the same direction, in 158.4 seconds, and the ratio of the length of Train N to the length of the platform is 9:5. If Train M's speed is 60 km/h and Train N moves faster than Train M, what is the difference in time taken for Train N to cross the same platform and for Train M to cross Train N moving in the opposite direction?

Length of train M = x Length of train N = y Speed of train M = 60 kmph Length of platform = a Speed of train N = z x + a = 60 * 5/18 * 60 x + a = 1000 x = (60 + 12) * 5/18 * 30 x = 600 m Length of platform = 1000 – 600 = 400 m Length of train N = 400 * 9/5 = 720 m 720 + 600 = (z – 60) * 5/18 * 158.4 z – 60 = 30 z = 90 kmph Time taken by train N crosses a platform = (400 + 720)/ (90 * 5/18) = 44.8 seconds Time taken by train M crosses train N = (720 + 600)/ ((90 + 60) * 5/18) = 31.68 seconds Required difference = 44.8 – 31.68 = 13.12 seconds