Question : A thief, seeing a policeman from a distance of 120 m, starts running at a speed of 7 km/hr. The policeman chases immediately with a speed of 8 km/hr and the thief is caught. What is the distance run by the thief?
Option 1: 820 m
Option 2: 780 m
Option 3: 840 m
Option 4: 800 m
Correct Answer: 840 m
Solution :
The relative speed of the policeman and the thief = 8 – 7 = 1 km/hr = 1 × $\frac{5}{18}$ m/s = $\frac{5}{18}$ m/s
The time it takes for the policeman to catch the thief = $\frac{120}{\frac{5}{18}}$ = 432 s
The speed of the thief = 7 km/hr = 7 × $\frac{5}{18}$ m/s = $\frac{35}{18}$ m/s
$\therefore$ The distance run by the thief = $\frac{35}{18}$ × 432 = 840 m
Hence, the correct answer is 840 m.
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