Multiple choice

A thief is 400m ahead of a policeman. The thief started running and the policeman started chasing simultaneously. Assuming the speed of thief be 10km/h & policeman be 15 km/h, calculate the distance (in metres) covered by thief before the policeman caught the thief.

  1. 750 m

  2. 800 m

  3. 850 m

  4. 900 m

  5. Na
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative speed = 15 - 10 = 5 km/h = 5 * (5/18) m/s = 25/18 m/s. Time to catch = distance / relative speed = 400 / (25/18) = 400 * 18 / 25 = 16 * 18 = 288 seconds. Distance covered by thief = speed * time = 10 * (5/18) * 288 = 10 * 5 * 16 = 800 m.

AI explanation

The relative speed of the policeman with respect to the thief is calculated by subtracting their speeds, giving 15 - 10 = 5 km/h. The time taken to catch the thief is found by dividing the gap of 400 meters (0.4 km) by the relative speed, which yields 0.08 hours. The distance covered by the thief in this time is his speed multiplied by the time, calculated as 10 * 0.08 = 0.8 km. Therefore, the thief covered a distance of 800 meters.

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