A policeman spots a thief 200 m ahead. The thief runs at 10 km/h and the policeman chases at 11 km/h. After 6 minutes of running, what is the distance between them (in metres)?
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A100 m
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B180 m
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C150 m
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D125 m
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ENone of these
Answer
Correct Answer: 100 m
Explanation
Introduction / Context:Pursuit problems use relative speed along a straight line. The gap closes at (chaser speed − runner speed). Once we find how much is closed in the given time, we subtract from the initial lead to get the remaining separation.
Given Data / Assumptions:
- Initial lead L = 200 m.
- Speeds: thief = 10 km/h, policeman = 11 km/h.
- Time t = 6 minutes = 360 s.
Concept / Approach:Relative speed = (11 − 10) km/h = 1 km/h. Convert 1 km/h to m/s: 1000/3600 ≈ 0.277777… m/s. Distance closed in time t equals relative_speed * t.
Step-by-Step Solution:
Relative speed = 0.277777… m/s.Closed distance = 0.277777… * 360 ≈ 100 m.Remaining gap = 200 − 100 = 100 m.Verification / Alternative check:In 6 minutes, thief covers (10 km/h)*(0.1 h)=1 km; policeman covers (11 km/h)*(0.1 h)=1.1 km; difference 0.1 km = 100 m—same result.
Why Other Options Are Wrong:180/150/125 m do not match the closed distance computed from the correct relative speed.
Common Pitfalls:Adding speeds when both move in the same direction; mixing metres and kilometres without proper conversion.
Final Answer:100 m