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A thief started running from point X at a speed of 20 km/hr, after running for 30 minutes, when he watched the police at the distance of 400 m coming from opposite direction at the speed of 30 km/hr, he turned and started running at 25 km/hr in the same direction as of police. After how much distance from point X police will catch the thief?
Correct answer is '8 km'. Can you explain this answer?
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Most Upvoted Answer
A thief started running from point X at a speed of 20 km/hr, after ru...
Given Information:
- Thief's initial speed = 20 km/hr
- Thief runs for 30 minutes before seeing the police
- Distance of police from the thief at that moment = 400 m
- Police's speed = 30 km/hr
- Thief's new speed after seeing the police = 25 km/hr
Approach:
1. Convert the time and speed to the same unit (kilometers per hour or meters per second) for easy calculation.
2. Calculate the distance covered by the thief in 30 minutes.
3. Calculate the time it takes for the police to cover the initial distance of 400 meters towards the thief.
4. Calculate the time it takes for the police to catch the thief after he starts running at 25 km/hr.
5. Calculate the distance covered by the police in that time.
Calculation:
1. Convert time and speed to kilometers per hour:
- Thief's initial speed = 20 km/hr
- Thief runs for 30 minutes = 30/60 = 0.5 hours
2. Distance covered by the thief in 30 minutes:
Distance = Speed × Time
Distance = 20 km/hr × 0.5 hr
Distance = 10 km
3. Time taken by the police to cover the initial distance of 400 meters:
Distance = Speed × Time
400 m = (30 km/hr) × Time
Time = 400 m / (30 km/hr) = (400/1000) km / (30/60) hr
Time = 0.8/0.5 hr = 1.6 hr
4. Time taken by the police to catch the thief after he starts running at 25 km/hr:
Relative speed = Police's speed - Thief's speed
Relative speed = 25 km/hr - 20 km/hr = 5 km/hr
Distance = Relative speed × Time
Distance = 5 km/hr × 1.6 hr = 8 km
Conclusion:
The police will catch the thief after a distance of 8 km from point X.
- Thief's initial speed = 20 km/hr
- Thief runs for 30 minutes before seeing the police
- Distance of police from the thief at that moment = 400 m
- Police's speed = 30 km/hr
- Thief's new speed after seeing the police = 25 km/hr
Approach:
1. Convert the time and speed to the same unit (kilometers per hour or meters per second) for easy calculation.
2. Calculate the distance covered by the thief in 30 minutes.
3. Calculate the time it takes for the police to cover the initial distance of 400 meters towards the thief.
4. Calculate the time it takes for the police to catch the thief after he starts running at 25 km/hr.
5. Calculate the distance covered by the police in that time.
Calculation:
1. Convert time and speed to kilometers per hour:
- Thief's initial speed = 20 km/hr
- Thief runs for 30 minutes = 30/60 = 0.5 hours
2. Distance covered by the thief in 30 minutes:
Distance = Speed × Time
Distance = 20 km/hr × 0.5 hr
Distance = 10 km
3. Time taken by the police to cover the initial distance of 400 meters:
Distance = Speed × Time
400 m = (30 km/hr) × Time
Time = 400 m / (30 km/hr) = (400/1000) km / (30/60) hr
Time = 0.8/0.5 hr = 1.6 hr
4. Time taken by the police to catch the thief after he starts running at 25 km/hr:
Relative speed = Police's speed - Thief's speed
Relative speed = 25 km/hr - 20 km/hr = 5 km/hr
Distance = Relative speed × Time
Distance = 5 km/hr × 1.6 hr = 8 km
Conclusion:
The police will catch the thief after a distance of 8 km from point X.
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Community Answer
A thief started running from point X at a speed of 20 km/hr, after ru...
Given,
Speed of thief before watching the police = 20 km/hr
Speed of thief after watching the police = 25 km/hr
Distance between police and thief = 400 m
We know that, Speed = Distance / Time
If speed of body A is x m/s and speed of body B is y m/s then
Relative speed of two bodies moving in same direction = (x − y) m/s
Relative speed of two bodies moving in opposite direction = (x + y) m/s
In 20 minutes, thief covered the distance from point X =20 × (30/60) km
= 10 km
Relative speed of police with respect to thief =(30 − 25) km/hr
= 5 km/hr
Time taken by police to cover 400 m or 0.4 km = 0.4/5 hr
= 0.08 hr
Distance covered by the thief in 0.08 hr = 25 × 0.08
= 2 km
Distance from Point X = (10 − 2) km
= 8 km
∴ Police will catch the thief at 8 km from point X.
Hence, the correct answer is 8 km.
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A thief started running from point X at a speed of 20 km/hr, after running for 30 minutes, when he watched the police at the distance of 400 m coming from opposite direction at the speed of 30 km/hr, he turned and started running at 25 km/hr in the same direction as of police. After how much distance from point X police will catch the thief?Correct answer is '8 km'. Can you explain this answer?
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A thief started running from point X at a speed of 20 km/hr, after running for 30 minutes, when he watched the police at the distance of 400 m coming from opposite direction at the speed of 30 km/hr, he turned and started running at 25 km/hr in the same direction as of police. After how much distance from point X police will catch the thief?Correct answer is '8 km'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A thief started running from point X at a speed of 20 km/hr, after running for 30 minutes, when he watched the police at the distance of 400 m coming from opposite direction at the speed of 30 km/hr, he turned and started running at 25 km/hr in the same direction as of police. After how much distance from point X police will catch the thief?Correct answer is '8 km'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thief started running from point X at a speed of 20 km/hr, after running for 30 minutes, when he watched the police at the distance of 400 m coming from opposite direction at the speed of 30 km/hr, he turned and started running at 25 km/hr in the same direction as of police. After how much distance from point X police will catch the thief?Correct answer is '8 km'. Can you explain this answer?.
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A thief started running from point X at a speed of 20 km/hr, after running for 30 minutes, when he watched the police at the distance of 400 m coming from opposite direction at the speed of 30 km/hr, he turned and started running at 25 km/hr in the same direction as of police. After how much distance from point X police will catch the thief?Correct answer is '8 km'. Can you explain this answer?, a detailed solution for A thief started running from point X at a speed of 20 km/hr, after running for 30 minutes, when he watched the police at the distance of 400 m coming from opposite direction at the speed of 30 km/hr, he turned and started running at 25 km/hr in the same direction as of police. After how much distance from point X police will catch the thief?Correct answer is '8 km'. Can you explain this answer? has been provided alongside types of A thief started running from point X at a speed of 20 km/hr, after running for 30 minutes, when he watched the police at the distance of 400 m coming from opposite direction at the speed of 30 km/hr, he turned and started running at 25 km/hr in the same direction as of police. After how much distance from point X police will catch the thief?Correct answer is '8 km'. Can you explain this answer? theory, EduRev gives you an
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