1. Given Data:
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Initial distance between Police and Culprit = 250 m
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Speed of Police (Sp) = 10 km/h
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Speed of Culprit (Sc) = 8 km/h
2. Calculate Relative Speed:
Since both are running in the same direction, the relative speed is the difference between their speeds:
Relative Speed=10−8=2 km/h
To match the distance unit (meters), convert km/h to m/s:
Relative Speed in m/s=2×185=95 m/s
3. Calculate Time taken to catch the culprit:
The police need to cover the initial gap of 250 m at the relative speed.
Time=Relative SpeedDistance
Time=5/9250=5250×9=50×9=450 seconds
4. Calculate Distance run by the Culprit:
The culprit ran for the same 450 seconds before being caught.
First, convert the culprit's speed to m/s:
Distanceculprit=Speedc×Time
Distanceculprit=920×450
Distanceculprit=20×50=1000 meters
5. Convert to Kilometers:
Conclusion:
The culprit had run 1 km before he was overpowered.
Correct Option: (b) 1 km
