Problems on Trains – Find train length from two platform times: A train takes 24 s to cross a 480 m platform and 36 s to cross a 900 m platform. What is the length of the train?

Introduction / Context:
Two crossing scenarios with different platform lengths allow us to eliminate speed and solve for train length directly. Represent total distance as (L_train + L_platform) = v * t in each case and subtract the equations.

Given Data / Assumptions:

• (L + 480) = v * 24.
• (L + 900) = v * 36.
• Uniform speed v.

Concept / Approach:
Subtracting the two equations removes L: (900 − 480) = v(36 − 24), yielding v. Substitute back to find L.

Step-by-Step Solution:
420 = v * 12 ⇒ v = 35 m/s.From L + 480 = 35 * 24 = 840 ⇒ L = 360 m.

Verification / Alternative check:
For the 900 m platform: L + 900 = 360 + 900 = 1260 m; time = 1260 / 35 = 36 s, valid.

Why Other Options Are Wrong:
400, 390, 430, 320 m will not satisfy both time equations simultaneously with one constant speed.

Common Pitfalls:
Adding times or lengths incorrectly; not recognizing that subtracting the equations isolates v immediately.

Final Answer:
360 m