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A and B start running together on a circular track in the same direction from point C. If the linear distance of both the runners from the starting point at time t minutes is same and the difference of the angle traversed by them at the centre is 120°, then after how much time (after they start from C) will they meet for the first time again at C?
- a)t minutes
- b)0.5f minutes
- c)2t minutes
- d)3f minutes
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A and B start running together on a circular track in the same directi...
From the diagram it is clear that the angle traversed by A or B should be double of that traversed by B or A.
Since the time taken is the same.
The speed of one is twice of the other.
Hence, they will meet again at the starting point 3f after they started running.
Hence, option 4.
Most Upvoted Answer
A and B start running together on a circular track in the same directi...
Given information:
- A and B start running together on a circular track in the same direction from point C.
- The linear distance of both runners from the starting point at time t minutes is the same.
- The difference of the angle traversed by them at the center is 120 degrees.
To find:
- After how much time (after they start from C) will they meet for the first time again at C?
Approach:
1. Let the circumference of the circular track be 'C' units.
2. Assume the linear speed of both runners to be 'v' units/minute.
3. As the linear distance of both runners from the starting point at time t minutes is the same, the distance covered by runner A in t minutes is vt units, and the distance covered by runner B in t minutes is vt units.
4. Since the circumference of the circular track is C, the distance covered by runner A in t minutes is vt = C + x, where x is the extra distance covered by runner A due to the difference in the angle traversed.
5. Similarly, the distance covered by runner B in t minutes is vt = C - x.
6. From the given information, the difference of the angle traversed by A and B at the center is 120 degrees. This implies that the extra distance covered by runner A, x, is the arc length of 120 degrees on the circular track.
7. The arc length of 120 degrees on a circle of radius r is given by (120/360) * 2πr = (1/3) * 2πr = (2/3)πr.
8. Equating the extra distance covered by runner A, x, to (2/3)πr, we get vt = (2/3)πr.
9. Solving for t, we have t = (2/3)πr/v.
Explanation:
The time taken for A and B to meet again at C will be (2/3)πr/v. Since the radius of the circular track is constant, the ratio of the distance covered to the linear speed is constant. Therefore, the time taken for A and B to meet again at C will be the same regardless of the radius of the circular track.
Answer:
The correct answer is option D) 3f minutes.
- A and B start running together on a circular track in the same direction from point C.
- The linear distance of both runners from the starting point at time t minutes is the same.
- The difference of the angle traversed by them at the center is 120 degrees.
To find:
- After how much time (after they start from C) will they meet for the first time again at C?
Approach:
1. Let the circumference of the circular track be 'C' units.
2. Assume the linear speed of both runners to be 'v' units/minute.
3. As the linear distance of both runners from the starting point at time t minutes is the same, the distance covered by runner A in t minutes is vt units, and the distance covered by runner B in t minutes is vt units.
4. Since the circumference of the circular track is C, the distance covered by runner A in t minutes is vt = C + x, where x is the extra distance covered by runner A due to the difference in the angle traversed.
5. Similarly, the distance covered by runner B in t minutes is vt = C - x.
6. From the given information, the difference of the angle traversed by A and B at the center is 120 degrees. This implies that the extra distance covered by runner A, x, is the arc length of 120 degrees on the circular track.
7. The arc length of 120 degrees on a circle of radius r is given by (120/360) * 2πr = (1/3) * 2πr = (2/3)πr.
8. Equating the extra distance covered by runner A, x, to (2/3)πr, we get vt = (2/3)πr.
9. Solving for t, we have t = (2/3)πr/v.
Explanation:
The time taken for A and B to meet again at C will be (2/3)πr/v. Since the radius of the circular track is constant, the ratio of the distance covered to the linear speed is constant. Therefore, the time taken for A and B to meet again at C will be the same regardless of the radius of the circular track.
Answer:
The correct answer is option D) 3f minutes.
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A and B start running together on a circular track in the same direction from point C. If the linear distance of both the runners from the starting point at time t minutes is same and the difference of the angle traversed by them at the centre is 120, then after how much time (after they start from C) will they meet for the first time again at C?a)t minutesb)0.5f minutesc)2t minutesd)3f minutesCorrect answer is option 'D'. Can you explain this answer?
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A and B start running together on a circular track in the same direction from point C. If the linear distance of both the runners from the starting point at time t minutes is same and the difference of the angle traversed by them at the centre is 120, then after how much time (after they start from C) will they meet for the first time again at C?a)t minutesb)0.5f minutesc)2t minutesd)3f minutesCorrect answer is option 'D'. 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 and B start running together on a circular track in the same direction from point C. If the linear distance of both the runners from the starting point at time t minutes is same and the difference of the angle traversed by them at the centre is 120, then after how much time (after they start from C) will they meet for the first time again at C?a)t minutesb)0.5f minutesc)2t minutesd)3f minutesCorrect answer is option 'D'. 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 and B start running together on a circular track in the same direction from point C. If the linear distance of both the runners from the starting point at time t minutes is same and the difference of the angle traversed by them at the centre is 120, then after how much time (after they start from C) will they meet for the first time again at C?a)t minutesb)0.5f minutesc)2t minutesd)3f minutesCorrect answer is option 'D'. Can you explain this answer?.
A and B start running together on a circular track in the same direction from point C. If the linear distance of both the runners from the starting point at time t minutes is same and the difference of the angle traversed by them at the centre is 120, then after how much time (after they start from C) will they meet for the first time again at C?a)t minutesb)0.5f minutesc)2t minutesd)3f minutesCorrect answer is option 'D'. 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 and B start running together on a circular track in the same direction from point C. If the linear distance of both the runners from the starting point at time t minutes is same and the difference of the angle traversed by them at the centre is 120, then after how much time (after they start from C) will they meet for the first time again at C?a)t minutesb)0.5f minutesc)2t minutesd)3f minutesCorrect answer is option 'D'. 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 and B start running together on a circular track in the same direction from point C. If the linear distance of both the runners from the starting point at time t minutes is same and the difference of the angle traversed by them at the centre is 120, then after how much time (after they start from C) will they meet for the first time again at C?a)t minutesb)0.5f minutesc)2t minutesd)3f minutesCorrect answer is option 'D'. Can you explain this answer?.
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ample number of questions to practice A and B start running together on a circular track in the same direction from point C. If the linear distance of both the runners from the starting point at time t minutes is same and the difference of the angle traversed by them at the centre is 120, then after how much time (after they start from C) will they meet for the first time again at C?a)t minutesb)0.5f minutesc)2t minutesd)3f minutesCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice CAT tests.
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