A thief, pursued by a policeman, was 100 m ahead at the start. If the ratio of the speed of the policeman to that of the thief was 5 : 4, then how far could the thief go before he was caught by the policeman ?

Solution(By Examveda Team)

Let the thief be caught x metres from the place where the policeman started running.
Let the speed of the policeman and the thief be 5y m/s and 4y m/s respectively.
Then, time taken by the policeman to cover x metres = time taken by the thief to cover (x - 100) m
$$\eqalign{ & \Rightarrow \frac{x}{{5y}} = \frac{{\left( {x - 100} \right)}}{{4y}} \cr & \Rightarrow 4x = 5\left( {x - 100} \right) \cr & \Rightarrow x = 500 \cr} $$
So, the thief ran (500 - 100) i.e., 400 m before being caught.