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:

Answer: Option A

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