After seeing a policeman from a distance of 500 m, a thief starts running at a speed of 10 km/h. After noticing, the policeman chases immediately with a speed of 12 km/h, and the thief is caught. The distance run by the policeman is:

3 km

Distance between police and the thief = 500m

= 0.5 km

Relative speed (when moves in same direction ) = 12 - 10 = 2 km/h

Time = \(\frac{Distance}{Speed}\)

= \(\frac{0.5}{2}\) = 0.25 hours

So , 0.25 hours are required to catch the thief .

Now Distance traveled by policeman = 12x

= 12 × 0.25 = 3 km

So , The distance run by the policeman is 3 km.