Express vs local – platform length from combined scenarios A 48 km/h train completely crosses an opposite 42 km/h train (half its length) in 12 s, and passes a platform in 45 s. Find the platform length.

Introduction / Context:
This composite problem first uses relative speed to deduce train length from a crossing event, then applies that length to find a platform length from a single-train crossing time. Handling multiple steps cleanly is the key skill.

Given Data / Assumptions:

• Train A speed = 48 km/h; Train B speed = 42 km/h; B length = A length / 2.
• They cross (opposite) in 12 s.
• Train A passes a platform in 45 s at 48 km/h.

Concept / Approach:
Opposite direction relative speed v_rel = 48 + 42 = 90 km/h = 25 m/s. Crossing time gives sum of lengths. Then use A's platform pass to compute platform length.

Step-by-Step Solution:

Verification / Alternative check:
Recompute crossing: A + B = 200 + 100 = 300 m; 300 / 25 m/s = 12 s, consistent.

Why Other Options Are Wrong:
450 m, 560 m, 600 m: Do not align with the computed 600 m traverse minus 200 m train length.

Common Pitfalls:
Using 48 km/h as 48 m/s or forgetting to halve the length of B. Maintain unit discipline.

Final Answer:
400 m