A thief running at speed of 'x' km/h is chased by a policeman running at a speed of 10 km/h. If the thief is ahead by 100 metres, the policeman catches the thief after 3 minutes. At what speed is the thief running ('x' being the unknown speed)?

8 km/h

Distance to cover by policeman = 100 m

Time taken to catch the thief = 3 minutes = 180 sec

Relative speed = ( 10 - x ) km/h

Relative speed = \(\frac{100}{180 }\) m/sec

x m/sec = x ×(\frac{18}{5 }\) km/h

= \(\frac{100}{180 }\)×(\frac{18}{5 }\)

= 2 km/h

Now ,

10 - x = 2

x = 8 km/h

So , speed of thief is 8km/h