A train crosses a pole in 10 s and a 200 m platform in 20 s. What is the length of the train (in metres)?

Introduction / Context:
Let the train length be L and speed be v (m/s). Passing a pole takes L/v seconds, while passing a platform of length P takes (L + P)/v seconds at the same speed. Using the two given times allows solving for L directly without computing v numerically first.

Given Data / Assumptions:

• Pole time = 10 s ⇒ L = 10v.
• Platform length P = 200 m; platform time = 20 s ⇒ L + 200 = 20v.

Concept / Approach:
Eliminate v by substituting L = 10v into the platform equation and solve for L. This exploits the same-speed condition across both scenarios.

Step-by-Step Solution:

Verification / Alternative check:
Check: time across platform = (L + 200)/v = (200 + 200)/20 = 20 s—consistent.

Why Other Options Are Wrong:
100/250/300 m contradict either the pole time or platform time at a single consistent speed.

Common Pitfalls:
Assuming 20 s implies double the length only; it is double total distance L + P, not L itself unless computed properly.

Final Answer:
200m