A thief is spotted by a policeman from a distance of 100 metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10km/hr, how far the thief will have run before he is overtaken?

1. A

   380 metres

2. B

   400 metres

3. C

   375 metres

4. D

   410 metres

Appeared in: RRB Staff Nurse Jaipur-6th June 2018

Explanation

• The problem is solved by determining the time it takes for the policeman to close the 100-meter gap, considering their relative speed.
• The relative speed is the difference between the policeman's speed and the thief's speed (10 - 8 = 2 km/hr).
• The time to catch is 180 seconds, calculated by dividing the initial distance (100 m) by the relative speed (after converting it to m/s).
• In these 180 seconds, the thief, running at 8 km/hr (or 20/9 m/s), covers a distance of 400 meters.

Why Other Options Were Wrong

• Option A: This value is incorrect. It may arise from a miscalculation, such as an error in converting units or calculating the time taken to catch the thief.
• Option C: This value is incorrect. It could be the result of an error in setting up the ratio of speeds and distances or a simple arithmetic mistake.
• Option D: This value is incorrect. A slight error in calculation, such as rounding numbers incorrectly during an intermediate step, might lead to this answer.

Related Visual

• Visual 1: Diagram - A diagram showing the initial positions of the policeman and the thief, the 100m gap, and arrows indicating their direction of motion and speeds. This helps visualize the chase scenario.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Relative Speed and Distance as background academic context rather than a clinical decision trigger.
• Understanding relative speed is crucial for solving problems where objects are moving in relation to each other.
• When objects move in the same direction, their relative speed is the difference between their individual speeds.
• When objects move in opposite directions, their relative speed is the sum of their individual speeds.

How to Approach the Question

• First, identify the knowns: the speeds of both individuals (policeman and thief) and the initial distance separating them.
• Recognize this as a relative speed problem where both individuals are moving in the same direction.
• Calculate the relative speed by subtracting the slower speed (thief's) from the faster speed (policeman's).
• Use the formula Time = Distance / Speed to find the time it takes for the policeman to cover the initial 100-meter gap using the calculated relative speed. Ensure all units are consistent (e.g., convert km/hr to m/s).
• Finally, calculate the distance the thief covered in that time using the formula Distance = Speed × Time.
• Alternatively, use the ratio of speeds (10:8 or 5:4) to determine the ratio of distances covered. The difference in the ratio (1 part) equals the initial gap (100m), allowing you to calculate the thief's distance (4 parts).

Concept Tested & Keywords

• Concept Tested: Relative Speed and Distance
• Stem keywords: thief, policeman, distance, 100 metres, speed, 8 km/hr, 10 km/hr
• Lead-in keywords: how far

Question ID

QocMUN6hAilxcEBdT4gFWF

Copy ID