Problems on Trains – Find train length from platform-crossing data: A passenger train runs at 72 km/h and crosses a 400 m long platform in 30 seconds. What is the length of the train?

Introduction / Context:
Crossing a platform requires the train to cover its own length plus the platform length. With speed and time known, total distance gives the sum, from which we deduce the train’s length.

Given Data / Assumptions:

• Speed = 72 km/h = 20 m/s.
• Time = 30 s.
• Platform length = 400 m.

Concept / Approach:
Total distance = speed * time = (L_train + L_platform). Solve for L_train.

Step-by-Step Solution:
Speed (m/s) = 72 * (1000/3600) = 20 m/s.Total distance = 20 * 30 = 600 m.Train length = 600 − 400 = 200 m.

Verification / Alternative check:
At 20 m/s, the train covers 200 m in 10 s and the platform in 20 s; total 30 s, matching the data.

Why Other Options Are Wrong:
150, 180, 220, 240 m cannot satisfy total distance 600 m with a 400 m platform.

Common Pitfalls:
Forgetting unit conversion or subtracting in the wrong order.

Final Answer:
200 m