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A and B run in opposite directions from a point P on the circumference of a circle with different but constant speeds. A runs in the clockwise direction. They meet for the first time at distance of 900m in the clockwise direction from P, and for the second time at a distance of 800m in the anticlockwise direction from P, and B is yet to complete one round. The circumference of the circle is:
- a)1700m
- b)1250m
- c)1300m
- d)1200m
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A and B run in opposite directions from a point P on the circumference...
By the time they meet for the second time, both of them, together, have completed exactly 2 rounds, since they are running at different speeds, one of them has completed more than one round and other is yet to complete a round. A runs 900m per meeting. Hence A ran 1800m by the time they met for the second time. B ran a total of 800 m by this time.
Cirumference = 1800 + 800 / 2 = 1300 m
Cirumference = 1800 + 800 / 2 = 1300 m
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A and B run in opposite directions from a point P on the circumference...
Given Information:
- A and B run in opposite directions from a point P on the circumference of a circle.
- A runs in the clockwise direction.
- They meet for the first time at a distance of 900m in the clockwise direction from P.
- They meet for the second time at a distance of 800m in the anticlockwise direction from P.
- B is yet to complete one round.
Approach:
- Let the speed of A be x m/s and the speed of B be y m/s.
- We need to find the circumference of the circle based on the given information.
First Meeting:
- Let the time taken by A to reach the first meeting point be t1 seconds.
- A covers a distance of 900m in the clockwise direction, so the distance covered by A in t1 seconds is 900m.
- B covers a distance of 900m in the anticlockwise direction in the same time, so the distance covered by B in t1 seconds is 900m.
- The relative speed of A and B is (x + y) m/s (as they are moving in opposite directions).
- Therefore, (x + y)t1 = 900.
Second Meeting:
- Let the time taken by A and B to reach the second meeting point be t2 seconds.
- A covers a distance of 800m in the anticlockwise direction, so the distance covered by A in t2 seconds is 800m.
- B covers a distance of 800m in the clockwise direction in the same time, so the distance covered by B in t2 seconds is 800m.
- The relative speed of A and B is (x + y) m/s (as they are moving in opposite directions).
- Therefore, (x + y)t2 = 800.
Calculating the Circumference:
- As B is yet to complete one round, the time taken by B to complete one round is the same as the time taken by A to cover the circumference of the circle.
- The distance covered by A in t1 seconds is equal to the distance covered by B in one round, which is the circumference of the circle.
- Therefore, xt1 = 2πr, where r is the radius of the circle.
- Similarly, xt2 = 2πr.
- Dividing the equations, we get t1/t2 = xt1/xt2 = 900/800.
- Therefore, (900/800) = (x + y)t1/(x + y)t2 = t1/t2.
- Simplifying, we get t1 = (9/8)t2.
Solving the Equations:
- From the first meeting, we have (x + y)t1 = 900.
- Substituting the value of t1 from the previous step, we get (x + y)(9/8)t2 = 900.
- Simplifying, we get (x + y)t2 = 800.
- Comparing this equation with the second meeting equation, we can say that t2 = t2.
- Therefore, (x + y)t2 = 800 = 800.
- Dividing both sides by t2, we get x + y = 1.
Finding the Circumference:
-
- A and B run in opposite directions from a point P on the circumference of a circle.
- A runs in the clockwise direction.
- They meet for the first time at a distance of 900m in the clockwise direction from P.
- They meet for the second time at a distance of 800m in the anticlockwise direction from P.
- B is yet to complete one round.
Approach:
- Let the speed of A be x m/s and the speed of B be y m/s.
- We need to find the circumference of the circle based on the given information.
First Meeting:
- Let the time taken by A to reach the first meeting point be t1 seconds.
- A covers a distance of 900m in the clockwise direction, so the distance covered by A in t1 seconds is 900m.
- B covers a distance of 900m in the anticlockwise direction in the same time, so the distance covered by B in t1 seconds is 900m.
- The relative speed of A and B is (x + y) m/s (as they are moving in opposite directions).
- Therefore, (x + y)t1 = 900.
Second Meeting:
- Let the time taken by A and B to reach the second meeting point be t2 seconds.
- A covers a distance of 800m in the anticlockwise direction, so the distance covered by A in t2 seconds is 800m.
- B covers a distance of 800m in the clockwise direction in the same time, so the distance covered by B in t2 seconds is 800m.
- The relative speed of A and B is (x + y) m/s (as they are moving in opposite directions).
- Therefore, (x + y)t2 = 800.
Calculating the Circumference:
- As B is yet to complete one round, the time taken by B to complete one round is the same as the time taken by A to cover the circumference of the circle.
- The distance covered by A in t1 seconds is equal to the distance covered by B in one round, which is the circumference of the circle.
- Therefore, xt1 = 2πr, where r is the radius of the circle.
- Similarly, xt2 = 2πr.
- Dividing the equations, we get t1/t2 = xt1/xt2 = 900/800.
- Therefore, (900/800) = (x + y)t1/(x + y)t2 = t1/t2.
- Simplifying, we get t1 = (9/8)t2.
Solving the Equations:
- From the first meeting, we have (x + y)t1 = 900.
- Substituting the value of t1 from the previous step, we get (x + y)(9/8)t2 = 900.
- Simplifying, we get (x + y)t2 = 800.
- Comparing this equation with the second meeting equation, we can say that t2 = t2.
- Therefore, (x + y)t2 = 800 = 800.
- Dividing both sides by t2, we get x + y = 1.
Finding the Circumference:
-
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A and B run in opposite directions from a point P on the circumference of a circle with different but constant speeds. A runs in the clockwise direction. They meet for the first time at distance of 900m in the clockwise direction from P, and for the second time at a distance of 800m in the anticlockwise direction from P, and B is yet to complete one round. The circumference of the circle is:a)1700mb)1250mc)1300md)1200mCorrect answer is option 'C'. Can you explain this answer?
Question Description
A and B run in opposite directions from a point P on the circumference of a circle with different but constant speeds. A runs in the clockwise direction. They meet for the first time at distance of 900m in the clockwise direction from P, and for the second time at a distance of 800m in the anticlockwise direction from P, and B is yet to complete one round. The circumference of the circle is:a)1700mb)1250mc)1300md)1200mCorrect answer is option 'C'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about A and B run in opposite directions from a point P on the circumference of a circle with different but constant speeds. A runs in the clockwise direction. They meet for the first time at distance of 900m in the clockwise direction from P, and for the second time at a distance of 800m in the anticlockwise direction from P, and B is yet to complete one round. The circumference of the circle is:a)1700mb)1250mc)1300md)1200mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B run in opposite directions from a point P on the circumference of a circle with different but constant speeds. A runs in the clockwise direction. They meet for the first time at distance of 900m in the clockwise direction from P, and for the second time at a distance of 800m in the anticlockwise direction from P, and B is yet to complete one round. The circumference of the circle is:a)1700mb)1250mc)1300md)1200mCorrect answer is option 'C'. Can you explain this answer?.
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Solutions for A and B run in opposite directions from a point P on the circumference of a circle with different but constant speeds. A runs in the clockwise direction. They meet for the first time at distance of 900m in the clockwise direction from P, and for the second time at a distance of 800m in the anticlockwise direction from P, and B is yet to complete one round. The circumference of the circle is:a)1700mb)1250mc)1300md)1200mCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for UGC NET.
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A and B run in opposite directions from a point P on the circumference of a circle with different but constant speeds. A runs in the clockwise direction. They meet for the first time at distance of 900m in the clockwise direction from P, and for the second time at a distance of 800m in the anticlockwise direction from P, and B is yet to complete one round. The circumference of the circle is:a)1700mb)1250mc)1300md)1200mCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A and B run in opposite directions from a point P on the circumference of a circle with different but constant speeds. A runs in the clockwise direction. They meet for the first time at distance of 900m in the clockwise direction from P, and for the second time at a distance of 800m in the anticlockwise direction from P, and B is yet to complete one round. The circumference of the circle is:a)1700mb)1250mc)1300md)1200mCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A and B run in opposite directions from a point P on the circumference of a circle with different but constant speeds. A runs in the clockwise direction. They meet for the first time at distance of 900m in the clockwise direction from P, and for the second time at a distance of 800m in the anticlockwise direction from P, and B is yet to complete one round. The circumference of the circle is:a)1700mb)1250mc)1300md)1200mCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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