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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

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 Correct Answer 3 min

Given:

Speed of the thief = 8 km/hr

Speed of the policeman = 10 km/hr

Formula used:

Time = Distance/Speed

Concept used:

If two bodies are moving in the same direction at u m/s and v m/s, (u > v)

Then the relative speed of the first body with respect to the second body = (u - v) m/s.

Calculation:

The relative speed between police and thief = (10 - 8) = 2 km/hr

⇒ 2 × (5/18) = (5/9) m/s

⇒ Distance between police and theif = 100 m

⇒ Time taken = Distance/Relative Speed

⇒ Time taken = 100/(5/9) = 180 sec

⇒ Time taken = 180/60 min = 3 minutes

∴ The time required for the policeman to catch the thief will be 3 minutes

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