UPSC Prelims 2013·CSAT·Quantitative Aptitude·Time, Speed and Distance

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

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Last updated 23 May 2026, 3:31 pm IST
  1. A2 min
  2. B3 minCorrect
  3. C4 min
  4. D6 min

Explanation

The correct answer is B. Here's a brief explanation: 1. Calculate the relative speed: The policeman is chasing the thief, so their relative speed is the difference between their speeds. Relative speed = Policeman's speed - Thief's speed = 10 km/hr - 8 km/hr = 2 km/hr. 2. Convert units for consistency: The distance is in meters (100 m) and the options are in minutes. Let's convert the relative speed from km/hr to m/min. 2 km/hr = 2 * 1000 meters / 60 minutes = 2000 m / 60 min = 100/3 m/min. 3. Calculate the time taken: Time = Distance / Relative Speed. Time = 100 m / (100/3 m/min) = 100 * (3/100) min = 3 minutes. Therefore, the policeman will catch the thief in 3 minutes. Analyzing the options: A) 2 min: Incorrect. This would imply a higher relative speed or a shorter distance. B) 3 min: Correct, as calculated above. C) 4 min: Incorrect. This would imply a lower relative speed or a longer distance. D) 6 min: Incorrect. This would imply a much lower relative speed or a significantly longer distance.
Quantitative Aptitude: A thief running at 8 km/hr is chased by a policeman whose speed is 10 km/hr. If the thief is 100 m ahead of the policema
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