Subject: General Aptitude · Chapter: Time and Distance · Exam: 2005 · Marks: · Difficulty:
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?
(a)80 m
(b)200 m
(c)400 m
(d)600 m
Answer
Answer (as printed): C
Explanation
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 $5 y$ m/s and $4 y$ m/s respectively. Then, time taken by the policeman to cover $x$ metres = time taken by the thief to cover $(x-100) \mathrm{m}$ $$\Rightarrow \frac{x}{5 y}=\frac{(x-100)}{4 y} \Rightarrow 4 x=5(x-100) \Rightarrow x=500 .$$ So, the thief ran (500-100) i.e. 400 m before being caught.
Explanation as extracted from the printed page; notation may be imperfect.