A train 130 meters long travelling at 54 km/hr crosses the bridge in 30 sec.…

Concept

When a train crosses a bridge (or platform), the train must travel a distance equal to its OWN length PLUS the length of the bridge, because the rear of the train only clears the far end after moving that combined distance. Distance = speed x time, and a speed in km/hr is converted to m/s by multiplying by 5/18.

Application

1. Convert the speed: 54 km/hr = 54 x 5/18 = 15 m/s.

2. Total distance covered while crossing = speed x time = 15 m/s x 30 s = 450 m.

3. This total distance equals train length + bridge length, so bridge length = 450 - 130 = 320 m.

Cross-check

Add the bridge length back to the train length: 320 + 130 = 450 m. At 15 m/s, covering 450 m takes 450 / 15 = 30 s, which matches the given time. So the bridge is 320 m long.