A man sees a train passing over a bridge $1$ km long. The length of the train is half that of the bridge. If the train clears the bridge in $2$ min, then the speed of the train is:

The length of the bridge is 1 km, or 1000 m, so the train is half that length, which is 500 m. Using the total distance formula for clearing a bridge, the train must cover 1000 m + 500 m = 1500 m in 2 minutes (120 seconds). Its speed is 1500 divided by 120, giving 12.5 meters per second. To convert to kilometers per hour, multiply by 18/5, which results in 45 km/hr. The speed of the train is 45 km/hr.

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