Question : A policeman saw a thief at a distance of 400 m. The thief started running at a speed of 10 km/h and the policeman chased him at 12 km/h in the same direction. At what distance from the starting point will the policeman catch the thief?
Option 1: 2.4 km
Option 2: 3 km
Option 3: 2 km
Option 4: 2.8 km
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Correct Answer: 2.4 km
Solution :
As time is constant, they cover the distance according to the ratio of their respective speeds.
Relative speed of the policeman = Speed of policeman – Speed of thief
= (12 – 10) km/h
= 2 km/h
Relative distance = 400 m = 0.4 Km
Time taken by a policeman to catch thief = $\frac{0.4}{2}$ = 0.2 hrs
$\therefore$ The policeman will catch the thief at a distance = 12 × 0.2 = 2.4 km
Hence, the correct answer is 2.4 km.
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