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Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30° at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds?
- a)6 : 5
- b)4 : 3
- c)6 : 1
- d)4 : 2
Correct answer is option 'A'. Can you explain this answer?
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Two persons, A and B are running on a circular track. At the start, B ...
Degrees at the center of the circle. If A runs at a faster pace than B, they will eventually meet at some point on the track. The question is – what is the angle at the center of the circle when they meet?
Let's assume that the length of the track is 1 unit. Then, the distance between A and B at the start is (1/12)π units, because the angle between their positions is 30 degrees out of 360 degrees, i.e. (30/360)π = (1/12)π radians.
Now, we know that A is faster than B, so A will cover more distance than B before they meet. Let's say A covers x units and B covers y units before they meet. Then, we have the following two equations:
x = y + (1/12)π (because A starts behind B)
x = 2π - y (because they meet after completing one full lap)
Solving for x and y, we get:
x = (23/24)π
y = (1/24)π
So, at the time they meet, A has covered (23/24)π units and B has covered (1/24)π units. Now, we can find the angle at the center of the circle using the following formula:
Angle = (Distance covered by A - Distance covered by B) / Radius
Since the radius of the circle is 1, we have:
Angle = (23/24)π - (1/24)π = (11/12)π
Therefore, the angle at the center of the circle when A and B meet is (11/12)π radians or approximately 285.6 degrees.
Let's assume that the length of the track is 1 unit. Then, the distance between A and B at the start is (1/12)π units, because the angle between their positions is 30 degrees out of 360 degrees, i.e. (30/360)π = (1/12)π radians.
Now, we know that A is faster than B, so A will cover more distance than B before they meet. Let's say A covers x units and B covers y units before they meet. Then, we have the following two equations:
x = y + (1/12)π (because A starts behind B)
x = 2π - y (because they meet after completing one full lap)
Solving for x and y, we get:
x = (23/24)π
y = (1/24)π
So, at the time they meet, A has covered (23/24)π units and B has covered (1/24)π units. Now, we can find the angle at the center of the circle using the following formula:
Angle = (Distance covered by A - Distance covered by B) / Radius
Since the radius of the circle is 1, we have:
Angle = (23/24)π - (1/24)π = (11/12)π
Therefore, the angle at the center of the circle when A and B meet is (11/12)π radians or approximately 285.6 degrees.
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Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30° at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds?a)6 : 5b)4 : 3c)6 : 1d)4 : 2Correct answer is option 'A'. Can you explain this answer?
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Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30° at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds?a)6 : 5b)4 : 3c)6 : 1d)4 : 2Correct answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30° at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds?a)6 : 5b)4 : 3c)6 : 1d)4 : 2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30° at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds?a)6 : 5b)4 : 3c)6 : 1d)4 : 2Correct answer is option 'A'. Can you explain this answer?.
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