A train takes 5 seconds to pass a pole. Its length is 120 m. How long (in seconds) will it take to cross a railway platform 180 m long?

Introduction / Context:The pole case reveals the train’s speed: crossing a pole in 5 seconds means the train covers its own length in 5 s. Use that speed to compute the time to cross a platform, where total distance equals train length plus platform length.

Given Data / Assumptions:

• L_train = 120 m; t_pole = 5 s ⇒ speed known.
• L_platform = 180 m.

Concept / Approach:Speed v_mps = L_train / t_pole = 120/5 = 24 m/s. For platform: S = 120 + 180 = 300 m. Time t = S / v_mps.

Step-by-Step Solution:

Verification / Alternative check:Proportion check: Platform adds 1.5× the train length; time scales from 5 s to 12.5 s, i.e., by factor 2.5—consistent since 300/120 = 2.5.

Why Other Options Are Wrong:7.5, 6.5, 10, 15 seconds do not match S/v with v from the pole data.

Common Pitfalls:Using only platform length; not extracting speed from the pole information.

Final Answer:12.5 seconds