A policeman goes after a thief who has 100 m start . If the policeman runs a km in 8 min and the thief runs a km in 10 min , then the distance covered by thief before he is being caught is :

400 m

Relative speed when they move in same direction 

Relative speed = \(\frac{1000}{8}\)  -  \(\frac{1000}{10}\)

                     =  \(\frac{5000-4000}{40}\)

                     =  \(\frac{1000}{40}\) m/minute

Required time = \(\frac{100}{\frac{1000}{40}}\) = 4 m/minute

Distance travelled by thief = \(\frac{1000  \; × \; 4 }{10}\) = 400m