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A and B start running in opposite directions from the same point along a circular track of circumference 600 m. They meet at Q for the first time and at P (which is 120 m away from Q) for the second time. B and C start running along the same track in opposite directions and meet at Q’ for the first time and at P’ (which is 150 m away from Q’) for the second time. If A and C run on the same track in opposite directions, find the number of distinct points at which they meet, excluding the starting point.(Speed of A < speed of B < speed of C)
Correct answer is '12'. Can you explain this answer?
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Verified Answer
A and B start running in opposite directions from the same point along...
Since gap between first and second meeting point of A and B is 120 m; and A is slower than B,
Time in which A runs 120 m is the same as time in which B runs 600 - 120 = 480 m Ratio of speeds of A and B is 1 : 4.
Similarly, time in which B runs 150 m is the same as time in which C runs 600 - 150 = 450 m
Ratio of speeds of B and C is 1 : 3.
Now when A and C run in opposite directions, their speeds are in the ratio 1:12.
When two persons are running in opposite directions along a circular track with their ratio of speeds as 1 : n, they meet at (n + 1) different points along the path including the starting point.
So, A and C meet at 12 + 1 = 13 points along the track (including the starting point). Since the starting point is to be ignored, they meet at 12 distinct points.
Answer: 12
Time in which A runs 120 m is the same as time in which B runs 600 - 120 = 480 m Ratio of speeds of A and B is 1 : 4.
Similarly, time in which B runs 150 m is the same as time in which C runs 600 - 150 = 450 m
Ratio of speeds of B and C is 1 : 3.
Now when A and C run in opposite directions, their speeds are in the ratio 1:12.
When two persons are running in opposite directions along a circular track with their ratio of speeds as 1 : n, they meet at (n + 1) different points along the path including the starting point.
So, A and C meet at 12 + 1 = 13 points along the track (including the starting point). Since the starting point is to be ignored, they meet at 12 distinct points.
Answer: 12
Most Upvoted Answer
A and B start running in opposite directions from the same point along...
Analysis
Let's analyze the problem step by step:
- A and B start running in opposite directions and meet at Q for the first time and at P (which is 120 m away from Q) for the second time.
- B and C start running in opposite directions and meet at Q for the first time and at P (which is 150 m away from Q) for the second time.
We need to find the number of distinct points at which A and C meet when they run on the same track in opposite directions.
Solution
To solve this problem, let's consider the time taken by each person to run from Q to P.
- From the given information, we know that B takes the same time to run from Q to P in both scenarios. Therefore, B's speed is constant.
- Let's assume the time taken by B to run from Q to P is t. Since the distance from Q to P is 120 m in the case of A and B, and 150 m in the case of B and C, we can set up the following equations:
Distance = Speed × Time
120 = Speed of A × t ...(1)
150 = Speed of C × t ...(2)
From equations (1) and (2), we can see that the ratio of the speeds of A and C is 120:150, which simplifies to 4:5.
Therefore, the speeds of A, B, and C can be represented as 4x, 5x, and 5y, respectively, where x and y are positive integers.
Since A and C are running in opposite directions, the relative speed between them is the sum of their speeds, which is (4x + 5y).
Finding the Number of Distinct Points of Intersection
To find the number of distinct points at which A and C meet, we need to find the number of times their relative speed becomes equal to the circumference of the circular track.
The relative speed of A and C is (4x + 5y). Let's find the values of x and y for which (4x + 5y) is a factor of 600.
- Factors of 600:
- 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
- We can see that (4x + 5y) is a factor of 600 for the following values of x and y:
- x = 25, y = 0 (gives 100)
- x = 20, y = 12 (gives 160)
- x = 15, y = 24 (gives 180)
- x = 10, y = 36 (gives 200)
- x = 5, y = 48 (gives 220)
- x = 0, y = 60 (gives 240)
Therefore, A and C will meet at 6 distinct points on the circular track, excluding the starting point. However, since A
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A and B start running in opposite directions from the same point along a circular track of circumference 600 m. They meet at Q for the first time and at P (which is 120 m away from Q) for the second time. B and C start running along the same track in opposite directions and meet at Q for the first time and at P (which is 150 m away from Q) for the second time. If A and C run on the same track in opposite directions, find the number of distinct points at which they meet, excluding the starting point.(Speed of A speed of B speed of C)Correct answer is '12'. Can you explain this answer?
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A and B start running in opposite directions from the same point along a circular track of circumference 600 m. They meet at Q for the first time and at P (which is 120 m away from Q) for the second time. B and C start running along the same track in opposite directions and meet at Q for the first time and at P (which is 150 m away from Q) for the second time. If A and C run on the same track in opposite directions, find the number of distinct points at which they meet, excluding the starting point.(Speed of A speed of B speed of C)Correct answer is '12'. 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 in opposite directions from the same point along a circular track of circumference 600 m. They meet at Q for the first time and at P (which is 120 m away from Q) for the second time. B and C start running along the same track in opposite directions and meet at Q for the first time and at P (which is 150 m away from Q) for the second time. If A and C run on the same track in opposite directions, find the number of distinct points at which they meet, excluding the starting point.(Speed of A speed of B speed of C)Correct answer is '12'. 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 in opposite directions from the same point along a circular track of circumference 600 m. They meet at Q for the first time and at P (which is 120 m away from Q) for the second time. B and C start running along the same track in opposite directions and meet at Q for the first time and at P (which is 150 m away from Q) for the second time. If A and C run on the same track in opposite directions, find the number of distinct points at which they meet, excluding the starting point.(Speed of A speed of B speed of C)Correct answer is '12'. Can you explain this answer?.
A and B start running in opposite directions from the same point along a circular track of circumference 600 m. They meet at Q for the first time and at P (which is 120 m away from Q) for the second time. B and C start running along the same track in opposite directions and meet at Q for the first time and at P (which is 150 m away from Q) for the second time. If A and C run on the same track in opposite directions, find the number of distinct points at which they meet, excluding the starting point.(Speed of A speed of B speed of C)Correct answer is '12'. 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 in opposite directions from the same point along a circular track of circumference 600 m. They meet at Q for the first time and at P (which is 120 m away from Q) for the second time. B and C start running along the same track in opposite directions and meet at Q for the first time and at P (which is 150 m away from Q) for the second time. If A and C run on the same track in opposite directions, find the number of distinct points at which they meet, excluding the starting point.(Speed of A speed of B speed of C)Correct answer is '12'. 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 in opposite directions from the same point along a circular track of circumference 600 m. They meet at Q for the first time and at P (which is 120 m away from Q) for the second time. B and C start running along the same track in opposite directions and meet at Q for the first time and at P (which is 150 m away from Q) for the second time. If A and C run on the same track in opposite directions, find the number of distinct points at which they meet, excluding the starting point.(Speed of A speed of B speed of C)Correct answer is '12'. Can you explain this answer?.
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A and B start running in opposite directions from the same point along a circular track of circumference 600 m. They meet at Q for the first time and at P (which is 120 m away from Q) for the second time. B and C start running along the same track in opposite directions and meet at Q for the first time and at P (which is 150 m away from Q) for the second time. If A and C run on the same track in opposite directions, find the number of distinct points at which they meet, excluding the starting point.(Speed of A speed of B speed of C)Correct answer is '12'. Can you explain this answer?, a detailed solution for A and B start running in opposite directions from the same point along a circular track of circumference 600 m. They meet at Q for the first time and at P (which is 120 m away from Q) for the second time. B and C start running along the same track in opposite directions and meet at Q for the first time and at P (which is 150 m away from Q) for the second time. If A and C run on the same track in opposite directions, find the number of distinct points at which they meet, excluding the starting point.(Speed of A speed of B speed of C)Correct answer is '12'. Can you explain this answer? has been provided alongside types of A and B start running in opposite directions from the same point along a circular track of circumference 600 m. They meet at Q for the first time and at P (which is 120 m away from Q) for the second time. B and C start running along the same track in opposite directions and meet at Q for the first time and at P (which is 150 m away from Q) for the second time. If A and C run on the same track in opposite directions, find the number of distinct points at which they meet, excluding the starting point.(Speed of A speed of B speed of C)Correct answer is '12'. Can you explain this answer? theory, EduRev gives you an
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