A train passes a man standing on a platform in 27 seconds and also passes a cyclist coming from opposite direction at 5 kmph in 24 seconds. How much time will the same train take to cross a 100 m long platform?

ATQ, Let the length of the train = x metres Let the speed of the train = y kmph Crossing a man: x = y * (5/18) * 27 = (135/18) y = (15/2) y Crossing a cyclist in opposite direction (speed = 5 kmph): Relative speed = (y + 5) kmph x = (y + 5) * (5/18) * 24 = (5 * 24 / 18)(y + 5) = (20/3)(y + 5) Equating both: (15/2) y = (20/3)(y + 5) Multiply both sides by 6: 45y = 40(y + 5) 45y = 40y + 200 5y = 200 y = 40 kmph Then, x = (15/2) * 40 = 300 m Speed in m/s = 40 * 5/18 = 100/9 m/s Required time to cross 100 m platform = (300 + 100) / (100/9) = 400 * 9 / 100 = 36 seconds