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/hr, what is the length of the platform?

Step 1: Understand the given data

• Time taken to pass the platform = 36 seconds
• Time taken to pass a man = 20 seconds
• Speed of the train = 54 km/h

Step 2: Convert speed to meters per second

Speed = 54 × (5 / 18) = 15 m/s

Step 3: Calculate length of the train

Length of train = Speed × Time to pass man
                = 15 × 20 = 300 meters

Step 4: Calculate total distance to pass the platform

Distance = Speed × Time to pass platform
         = 15 × 36 = 540 meters

Step 5: Calculate the length of the platform

Length of platform = Total distance - Length of train
                   = 540 - 300 = 240 meters

Answer: 240 meters

The length of the platform is 240 meters.

This question tests your ability to apply the formula Distance = Speed × Time in multiple contexts. By first finding the train’s length (using the time to pass a standing man), and then using the total time to pass a platform, we deduce the platform’s length. This type of question is common in competitive exams and helps strengthen concepts in speed, time, and distance.