A thief seeing a policeman at a distance of 150 metres starts running at 10 kmph and the policeman gives immediate chase at 12 kmph. When the thief is overtaken the thief has traveled a distance of:

Solution(By Examveda Team)

P__150m___T______x m (Let)_______Q.
Let Policeman caught thief at a distance (x + 150)m. And Thief has traveled x m.
Speed of Policeman
$$\eqalign{ & = 12\,\,{\text{kmph}} \cr & = \frac{{12 \times 5}}{{18}} \cr & = \frac{{60}}{{18}}\,\,{\text{m/sec}} \cr} $$
Speed of thief
$$\eqalign{ & = 10\,\,{\text{km}} \cr & = \frac{{10 \times 5}}{{18}} \cr & = \frac{{50}}{{18}}\,\,{\text{m/sec}} \cr} $$
In this case time is constant means Policeman covered (x + 150)m in same time thief covered x m.
Thus,
$$\eqalign{ & \frac{{{\text{Speed of the thief}}}}{{{\text{Speed of Policeman}}}} = \frac{x}{{150 + x}} \cr & \Rightarrow \frac{{50}}{{60}} = \frac{x}{{150 + x}} \cr & \Rightarrow 7500 + 50x = 60x \cr & \Rightarrow 10x = 7500 \cr & \Rightarrow x = 750\,{\text{m}} \cr} $$
So, Thief has traveled 750 m before the caught.