Synopsis IAS

Answer

Solution

UPSC Prelims

Mathematics

Theme:

Speed, Time and Distance / गति, समय और दूरी

Q35 2013, Speed, Time 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

8 किमी/घंटे की चाल से दौड़ते हुए चोर का पीछा 10 किमी/घंटे की चाल से दौड़ता हुआ पुलिसवाला कर रहा है। यदि चोर पुलिसवाले से 100 मीटर आगे है, तो चोर को पकड़ने में पुलिसवाले को कितना समय लगेगा ?

Explanation

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Correct Answer: b: 3 min
To solve this problem, we need to determine how long it will take for the policeman to catch up to the thief. We can do this by calculating the relative speed between the two and using the distance between them.
     Step 1: Convert the speeds from km/hr to m/s for easier calculation.
         ○ Thief's speed: 8 km/hr = \( \frac{8 \times 1000}{60 \times 60} \) m/s = \( \frac{20}{9} \) m/s
         ○ Policeman's speed: 10 km/hr = \( \frac{10 \times 1000}{60 \times 60} \) m/s = \( \frac{25}{9} \) m/s
     Step 2: Calculate the relative speed.
         ○ Relative speed = Policeman's speed - Thief's speed
         ○ Relative speed = \( \frac{25}{9} \) m/s - \( \frac{20}{9} \) m/s = \( \frac{5}{9} \) m/s
     Step 3: Use the relative speed to find the time required to cover the distance of 100 meters.
         ○ Distance = 100 meters
         ○ Time = Distance / Relative Speed
         ○ Time = \( \frac{100}{\frac{5}{9}} \) seconds = \( 100 \times \frac{9}{5} \) seconds = 180 seconds
     Step 4: Convert the time from seconds to minutes.
         ○ Time = 180 seconds = 3 minutes
     Therefore, the time required for the policeman to catch the thief is 3 minutes.

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Q 35. 2013, Speed, Time and Distance

Mathematics

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