Multiple choice

A thief saw a policeman, and he started running at a speed of 18 m/s. After 12 seconds, the policeman starts running behind the thief at a certain speed. If the policeman covered 864 meters distance to reach the thief, then the speed (in m/s) of the policeman is:

  1. 15

  2. 30

  3. 24

  4. 28
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Thief runs for 12s at 18m/s, distance = 216m. Policeman covers 864m. Time taken by policeman = t. Time taken by thief = t + 12. Distance of thief = 18 * (t + 12) = 216 + 18t. Total distance of thief = 216 + 18t = 864. 18t = 648, t = 36s. Speed of policeman = 864 / 36 = 24 m/s.

AI explanation

In 12 seconds, the thief covers a distance of 18 m/s * 12 s = 216 metres. When the policeman starts, the relative distance to close is 864 - 216 = 648 metres; since the policeman runs the entire 864 metres to catch the thief, let his speed be v m/s. The time taken by the policeman is 864/v, during which the thief travels an additional 18 * (864/v) metres, yielding the equation 864 = 216 + 18 * (864/v). Solving this gives 648 = 15552/v, so v is 24 m/s.

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