Question : A thief is spotted by a policeman from a distance of 400 m. When the policeman starts chasing, the thief also starts running. If the speed of the thief is 32 km/h and that of the policeman is 40 km/h, then how far would the thief have run before he is overtaken?
Option 1: 1500 m
Option 2: 1000 m
Option 3: 1200 m
Option 4: 1600 m
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Correct Answer: 1600 m
Solution :
Given: A thief is spotted by a policeman from a distance of 400 m. The speed of the thief is 32 km/h and that of the policeman is 40 km/h.
The relative speed of the policeman to the thief = (40 – 32) = 8 km/h.
8 km/h = $8×\frac{1000}{3600}=\frac{20}{9}$ m/sec.
Time taken by policeman to overtake the thief = $\frac{400}{\frac{20}{9}}=180$ sec.
Distance travelled by the thief in this time = $32×\frac{1000}{3600}×180=1600$ m.
Hence, the correct answer is 1600 m.
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