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

examrobotsa's picture

Submitted by examrobotsa on

Q: 140 (IAS/1995)
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

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,6,10,4,2,4,6

keywords: 

{'policeman': [0, 1, 0, 0], 'minutes': [0, 0, 1, 1], 'thief': [0, 1, 0, 0], 'speed': [0, 1, 2, 0], 'metres': [0, 1, 1, 0], 'km': [0, 0, 2, 1], 'time': [2, 6, 15, 23], 'hr': [0, 1, 2, 1]}

The policeman is moving at a faster speed than the thief, so he will eventually catch up. To find the time it takes for this to occur, we need to calculate the relative speed and the distance between them. The relative speed is the difference between their speeds, which is 10 km/hr - 8 km/hr = 2 km/hr. This speed represents the rate at which the policeman is gaining on the thief. The distance of 100 metres is the initial gap between them. We convert this distance to kilometres, which is 0.1 km.

To find the time, divide the distance by the relative speed: 0.1 km / 2 km/hr = 0.05 hours. Converting to minutes (since 1 hour is 60 minutes), the time is 0.05*60 = 3 minutes.

Option 1, 2, and 3 are not correct, because each wrongly estimates the time it will take for the policeman to catch up with the thief. The correct answer is option 4, which accurately calculates the time based on the relative speed and the distance between the policeman and the thief.