Question

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/h, then find the length of the platform.

• A. 225 m
• B. 235 m
• C. 230 m
• D. 240 m

Answer 1

The Correct Option is D

To solve this problem, we first need to determine the length of the train. We'll use the speed of the train and the time it takes to pass the man to find the train's length. Then, the total distance covered when passing the platform will include both the train and platform lengths.

1. Convert speed: The train's speed is 54 km/h. Convert this speed into meters per second (m/s) to match the time given in seconds.
   Speed in m/s = \( \frac{54 \times 1000}{3600} = 15 \text{ m/s} \)
2. Length of the train: The train takes 20 seconds to pass the man, which means the entire length of the train is covered during this time.
   Distance = Speed × Time = \( 15 \times 20 = 300 \text{ meters} \)
3. Total distance passed when crossing the platform: The train takes 36 seconds to pass the station platform. During this time, it covers the length of both the train and the platform.
   Total Distance = Speed × Time = \( 15 \times 36 = 540 \text{ meters} \)
4. Calculate the length of the platform: The platform length is the total distance minus the train length.
   Platform Length = Total Distance - Train Length = \( 540 - 300 = 240 \text{ meters} \)

The length of the platform is 240 meters.