Question : A thief is noticed by a policeman from a distance of 150 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 8 km/hr and 10 km/hr respectively. At what distance will the policeman catch the thief?
Option 1: 1000 metres
Option 2: 850 metres
Option 3: 500 metres
Option 4: 750 metres
Correct Answer: 750 metres
Solution :
The relative speed of policeman to the thief = (10 – 8) = 2 km/hr = $\frac{2×5}{18}$ = $\frac{5}{9}$ m/s
The time taken by the police to catch the thief = $150\div\frac{5}{9}$ = 270 seconds
Now, the speed of the policeman = 10 km/hr = $\frac{10×5}{18}$ = $\frac{25}{9}$ m/s
So, the distance travelled by the policeman in 270 seconds = $\frac{25}{9}×270$ = 750 metres
Hence, the correct answer is 750 metres.
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