Question : A thief is spotted by a constable from 200 m. When the constable starts the chase, the thief also starts running. If the speed of the constable is 8 km/h and the thief runs at the speed of 6 km/h, then how far (in m) will the thief be able to run before he is overtaken?
Option 1: 600
Option 2: 400
Option 3: 550
Option 4: 500
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Correct Answer: 600
Solution : Distance = 200 m Speed of thief = 6 km/h = $6\times{\frac{5}{18}}$ = $\frac{15}{9}$ m/s Speed of constable = 8 km/h = $8\times{\frac{5}{18}}$ = $\frac{20}{9}$ m/s Relative speed of constable = $(8−6)\times{\frac{5}{18}}$ = $\frac{5}{9}$ m/s To catch the thief, the policeman has to gain 200 m. Time taken to catch the thief = $\frac{200\times9}{5}$ = 360 s $\therefore$ Distance covered by the thief = $360\times{\frac{15}{9}}$ = 600 m Hence the correct answer is 600.
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