Multiple choice

A train running at 60 Km/hr takes 27 seconds to cross a platform. The same train takes 6 seconds to cross a man walking towards it at the speed of 12 Km/hr. Find the length of the platform.

  1. 120m

  2. 220m

  3. 330m

  4. 400m

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Train speed = 60 km/h = 50/3 m/s. Man speed = 12 km/h = 10/3 m/s. Relative speed = 50/3 + 10/3 = 60/3 = 20 m/s. Train length = 20 * 6 = 120 m. Crossing platform: (120 + P) / (50/3) = 27. 120 + P = 27 * 50 / 3 = 450. P = 330 m.

AI explanation

First, convert the speeds by multiplying 60 by 5/18 to get 50/3 m/s for the train, and 12 by 5/18 to get 10/3 m/s for the man. Since the man walks towards it, the relative speed is the sum of their speeds, giving 60/3 or 20 m/s. The length of the train is 20 m/s multiplied by the 6 seconds it takes to cross the man, which equals 120 meters. The total distance to cross the platform is the train speed of 50/3 m/s multiplied by 27 seconds, equaling 450 meters. Subtracting the train length of 120 meters from the 450 meter total distance gives the platform length. The result is 330m.

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