A train travelling at 36 km/h completely crosses another train that has half its length and is coming from the opposite direction at 54 km/h in 12 seconds. The same train passes a railway platform in 1.5 minutes. Find the length of the platform (in metres).

Introduction / Context:This mixes two standard train problems: first find the train’s own length using an “opposite direction” crossing, then use that length and known speed to compute platform length from a platform crossing time.

Given Data / Assumptions:

• Our train speed v = 36 km/h = 10 m/s.
• Other train speed = 54 km/h.
• Other train length = (1/2)*our train length.
• Crossing time (trains) = 12 s; platform time = 1.5 min = 90 s.

Concept / Approach:Opposite direction ⇒ relative speed = 36 + 54 = 90 km/h = 25 m/s. If our train length is L, other is L/2; total distance to clear each other = 1.5L.

Step-by-Step Solution:

Verification / Alternative check:Units are consistent (metres and seconds). Magnitudes are realistic for a moderate-speed train and a long platform segment.

Why Other Options Are Wrong:560, 620, 650, 750 m do not satisfy both crossing conditions simultaneously.

Common Pitfalls:Using only our train’s length in the first crossing; forgetting to convert km/h to m/s; misreading 1.5 minutes as 1.5 seconds.

Final Answer:700 metres