Problems on Trains – Train length equals platform length: A train travels at 72 km/h and takes 2 minutes to cross a platform whose length equals the length of the train. What is the length of the train?

Introduction / Context:When the platform length equals the train length L, the total distance to fully clear the platform is L + L = 2L. With the crossing time and speed, we can compute 2L and hence L.

Given Data / Assumptions:

• Speed = 72 km/h = 20 m/s.
• Crossing time = 2 minutes = 120 s.
• Platform length = train length = L.

Concept / Approach:Distance covered in crossing = 2L = speed * time. Then solve for L.

Step-by-Step Solution:Speed (m/s) = 20 m/s.Distance in 120 s = 20 * 120 = 2400 m.Hence 2L = 2400 ⇒ L = 1200 m.

Verification / Alternative check:If L = 1200 m, the platform is 1200 m too, so total 2400 m. At 20 m/s, time = 2400/20 = 120 s (2 minutes), consistent.

Why Other Options Are Wrong:600, 800, 900, 1000 m would not yield a 2-minute crossing at 72 km/h when the platform equals the train length.

Common Pitfalls:Using only one L instead of 2L; converting 2 minutes incorrectly; misreading km/h to m/s.

Final Answer:1200 m