A thief running at 8 km/hr is chased by a policeman whose speed is 10 km/hr. If the thief is 100 metres ahead of the policeman, then the time required for the policeman to catch the thief will be

To solve this problem, we use the concept of relative speed. Since both the policeman and the thief are running in the same direction, the relative speed is the difference between their speeds. Relative speed equals 10 km per hr minus 8 km per hr, which is 2 km per hr. To convert this speed into metres per minute, we multiply 2 by 1000 to get metres and divide by 60 to get minutes. So, the relative speed is 2000 divided by 60, which simplifies to 100 divided by 3 metres per minute. The distance to be covered is 100 metres. Time is calculated by dividing distance by speed. Therefore, time equals 100 divided by the fraction 100 over 3. This is equivalent to 100 multiplied by 3 divided by 100. The 100s cancel out, leaving us with 3 minutes. Thus, the policeman will catch the thief in 3 minutes. The correct option is D.