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

Correct Option (2)

To determine the time required for the policeman to catch the thief, the concept of relative speed is applied. The thief's speed is 8 km/hr, and the policeman's speed is 10 km/hr. Since the policeman is chasing the thief in the same direction, their relative speed is the difference between their individual speeds:

• Relative Speed = Speed of Policeman - Speed of Thief
• Relative Speed = 10 km/hr - 8 km/hr = 2 km/hr

The initial distance between them is 100 meters. To calculate the time in minutes, the relative speed must be converted from kilometers per hour (km/hr) to meters per minute (m/min):

• 1 km = 1000 m
• 1 hour = 60 minutes
• Relative Speed = 2 km/hr = (2 × 1000 m) / (60 min) = 2000/60 m/min = 100/3 m/min

Now, the time taken to cover the 100 m gap can be calculated using the formula Time = Distance / Speed:

• Time = 100 m / (100/3 m/min)
• Time = 100 × (3/100) minutes
• Time = 3 minutes

Therefore, the policeman will catch the thief in 3 minutes.

Incorrect Options:

Options 1 (2 min), 3 (4 min), and 4 (6 min) are incorrect. The precise calculation based on the relative speed of 100/3 m/min and the initial distance of 100 m yields a time of 3 minutes. These alternative options do not correspond with the accurate application of relative motion principles and unit conversions required to solve the problem.