A train passes a pole in 10 seconds and a 120 m platform in 18 seconds. What is the length of the train (in metres)?

Introduction / Context:
Let L be the train length and v its speed. Passing a pole takes time to cover just L; passing a platform of length P takes time to cover L + P at the same speed v.

Given Data / Assumptions:

• Pole time = 10 s ⇒ L = v * 10.
• Platform = 120 m, platform time = 18 s ⇒ L + 120 = v * 18.

Concept / Approach:
Eliminate v by dividing equations or substituting v = L/10 into the platform equation to solve for L directly.

Step-by-Step Solution:

Verification / Alternative check:
Speed v = L/10 = 15 m/s; platform pass distance = 270 m; 270/15 = 18 s, consistent.

Why Other Options Are Wrong:
130/180/240 m violate either the pole or platform timing when checked with the same v.

Common Pitfalls:
Adding 120 m incorrectly or mixing seconds with metres without using speed.

Final Answer:
150 m