Question : A policeman follows a thief, who is 1250 m ahead of him. The policeman and the thief run at speeds of 10 km/h, and 8 km/ h respectively. The distance (in km) run by the thief before he is nabbed by the policeman is:
Option 1: 7 km
Option 2: 4 km
Option 3: 5 km
Option 4: 6 km
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Correct Answer: 5 km
Solution : Given: Distance between the policeman and the thief = 1250 m Speed of the policeman = 10 km//h = $10×\frac{5}{18}=\frac{25}{9}$ m/s Speed of the thief = 8 km//h = $8×\frac{5}{18}=\frac{20}{9}$ m/s Relative speed of the policeman and the thief $=\frac{25}{9}–\frac{20}{9}=\frac{5}{9}$ m/s Time taken by the policeman to catch the thief $=\frac{1250}{\frac{5}{9}}=2250$ sec Distance travelled by thief before getting caught $=\frac{20}{9}×2250$ = 5000 m = 5 km Hence, the correct answer is 5 km.
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