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.