Question : A thief, seeing a policeman from a distance of 400 m, started running at a speed of 16 km/hr. The policeman chased him immediately at a speed of 18 km/hr and the thief was caught. What was the distance run by the thief before he was caught by the policeman?
Option 1: 3200 m
Option 2: 3230 m
Option 3: 3240 m
Option 4: 3220 m
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Correct Answer: 3200 m
Solution :
Thief's speed = 16 km/hr = $16×\frac{5}{18}=\frac{40}{9}$ m/s
Policeman's speed = 18 km/hr = $18×\frac{5}{18}=5$ m/s
Required distance = $\frac{\text{Difference × Slower speed}}{\text{Faster speed – Slower speed}}$
So, distance $=\frac{400×\frac{40}{9}}{5-\frac{40}{9}}=400×\frac{40}{9}×\frac{9}{5}=3200$ m
Hence, the correct answer is 3200 m.
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