A train speeds past a pole in 15 seconds and passes a 100 m long platform in 25 seconds. What is the length of the train (in meters)?

Introduction / Context:
Time to pass a pole equals train length divided by speed. Time to pass a platform equals (train length + platform length) divided by the same speed. Two equations let us solve for the train length directly.

Given Data / Assumptions:

• Pole time = 15 s → L = v * 15.
• Platform length = 100 m; platform time = 25 s → L + 100 = v * 25.

Concept / Approach:
Eliminate v: subtract the first relation from the second to find v, then back-substitute to get L.

Step-by-Step Solution:
(L + 100) − L = v(25 − 15) → 100 = 10v → v = 10 m/s.L = v * 15 = 10 * 15 = 150 m.

Verification / Alternative check:
Check platform time: (150 + 100)/10 = 25 s, matches.

Why Other Options Are Wrong:
200 m corresponds to a different speed; 50 m is too short; “Data inadequate” is incorrect because we have two independent equations.

Common Pitfalls:
Forgetting that platform time includes both train and platform lengths.

Final Answer:
150