Question : A policeman spots a thief at a distance of 360 m. Both the policeman and the thief simultaneously start running, with the former chasing the latter. While the thief runs at the speed of 8 km/h, the policeman runs at 9.2 km/h. How many metres will the policeman have to run before he catches up with the thief?
Option 1: 2852
Option 2: 2714
Option 3: 2668
Option 4: 2760
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Correct Answer: 2760
Solution : Speed of thief = 8 km/h Speed of policeman = 9.2 km/h Relative speed of policeman with respect to thief = 9.2 – 8 = 1.2 km/h Relative distance the policeman needs to cover = 360 m = 0.36 km Time taken by policeman to catch the thief =$\frac{\text{Relative Distance}}{\text{Relative Speed}}$ = $\frac{0.36}{1.2}$ = 0.3 hr So, total distance covered by policeman = Speed × Time = 9.2 × 0.3 km = 2.76 km = 2760 m Hence, the correct answer is 2760.
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