A train is crossing a platform of length 200 meters in 45 seconds and man standing on the platform in 25 seconds. If a man moves in the direction of the train with a speed of 2 meters per second, then the time taken by the train to cross him is

Given:

Length of platform = 200 meters

Time taken to cross platform = 45 seconds

Time taken to cross a stationary man = 25 seconds

Speed of the man = 2 meters/second

Formula used:

Speed of train = Distance / Time

Relative speed = Speed of train - Speed of man (since both move in the same direction)

Time taken to cross the moving man = Length of train / Relative speed

Calculation:

Speed of train = Length of platform / Time taken to cross platform

⇒ Speed of train = 200 / 45

⇒ Speed of train = 40 / 9 meters/second

Length of train = Speed of train × Time taken to cross stationary man

⇒ Length of train = (40 / 9) × 25

⇒ Length of train = 1000 / 9 meters

Relative speed = Speed of train - Speed of man

⇒ Relative speed = (40 / 9) - 2

⇒ Relative speed = (40 / 9) - (18 / 9)

⇒ Relative speed = 22 / 9 meters/second

Time taken to cross the moving man = Length of train / Relative speed

⇒ Time = (1000 / 9) / (22 / 9)

⇒ Time = 1000 / 22

⇒ Time = 250 / 55

⇒ Time = 31(1/4) seconds

∴ The correct answer is option (2).