Question : A policeman starts chasing a thief when he is already 600 metres ahead. If the policeman is running at a speed of 9 km/hr and the thief at 8 km/hr, then the thief would be caught at a distance of:
Option 1: 6.5 km
Option 2: 6 km
Option 3: 5 km
Option 4: 5.4 km
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Correct Answer: 5.4 km
Solution : Thief's speed = 8 km/hr = $8×\frac{5}{18}$ = $\frac{20}{9}$ m/s Policeman's speed = 9 km/h = $9×\frac{5}{18}=\frac{5}{2}$ m/s Distance $=\frac{\text{Difference of distance × Faster speed}}{\text{Faster speed – Slower speed}}$ $=\frac{600×\frac{5}{2}}{\frac{5}{2}-\frac{20}{9}}=600×\frac{5}{2}×\frac{18}{5}=5400$ m $= 5.4$ km Hence, the correct answer is 5.4 km.
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