Problems on Trains – Crossing a moving man (opposite direction): A 270 m train moves at 25 km/h and meets a man walking toward it at 2 km/h. In how many seconds will the train completely pass the man?

Introduction / Context:
When objects move toward each other, their relative speed is the sum of their individual speeds (with consistent units). To pass a man, the train must cover only its own length relative to the man.

Given Data / Assumptions:

• L_train = 270 m.
• Train speed = 25 km/h.
• Man speed (opposite) = 2 km/h.

Concept / Approach:
Relative speed = (25 + 2) km/h = 27 km/h. Convert to m/s by multiplying by 1000/3600 = 5/18.

Step-by-Step Solution:
Relative speed = 27 * (5/18) = 7.5 m/s.Time = distance / relative speed = 270 / 7.5 = 36 s.

Verification / Alternative check:
At 7.5 m/s, 36 s produces 270 m, which matches the train length and thus completes the pass.

Why Other Options Are Wrong:
32, 28, 24, 30 s correspond to incorrect relative speeds or arithmetic errors.

Common Pitfalls:
Subtracting speeds instead of adding; forgetting to convert km/h to m/s consistently.

Final Answer:
36 seconds