Question : A thief running at a speed of ‘$x$’ km/hr is chased by a policeman running at a speed of 10 km/hr. If the thief is ahead by 100 metres, the policeman catches the thief after 3 minutes. At what speed is the thief running (‘$x$’ being the unknown speed)?
Option 1: 4 km/hr
Option 2: 8 km/hr
Option 3: 10 km/hr
Option 4: 6 km/hr
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Correct Answer: 8 km/hr
Solution : Let the speed of the thief be $x$ km/hr. Speed of the policeman = 10 km/hr Time taken by a policeman to catch the thief = 3 minutes = $\frac{1}{20}$ hr Relative distance to be covered by policeman = 100 metres = 0.1 km So, Relative speed × Relative time = Relative distance $⇒(10-x) × \frac{1}{20} = 0.1$ $⇒(10-x) = 2$ $\therefore x= 8$ Hence, the correct answer is 8 km/hr.
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