Question : A policeman chases a thief. The speeds of the policeman and the thief are 8 km/hr and 6 km/hr, respectively. If the policeman starts 10 minutes late, at what distance he will catch the thief?
Option 1: 6 km
Option 2: 8 km
Option 3: 4 km
Option 4: 2 km
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Correct Answer: 4 km
Solution :
The thief starts running and the policeman chases him after 10 minutes.
The thief and the policeman run 6 km/hr and 8 km/hr, respectively.
Their relative speed $=8 - 6= 2$ km/hr
Distance covered by the thief in 10 minutes = $6\times \frac{10}{60} = 1$ km
Time required to catch the thief = $\frac{1}{2} = 0.5$ hour
$\therefore$ Distance covered by the policeman in 0.5 hours = $0.5 \times8 = 4$ km
So, the policeman will catch the thief at 4 km.
Hence, the correct answer is 4 km.
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