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A and B travel around a circular track at uniform speeds in opposite directions starting from diametrically opposite points. If they start at the same time, meet first after B has travelled 100 m and meet a second time 60 m before A completes one lap, then the circumference of the track in metres is
- a)400
- b)440
- c)420
- d)480
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A and B travel around a circular track at uniform speeds in opposite ...
Let's assume the circumference of the circular track is 'C' meters and the speeds of A and B are 'vA' and 'vB' meters per second respectively.
First Meeting:
In the first meeting, B has traveled 100 meters. Since they are moving in opposite directions, the total distance covered by A and B together is equal to the circumference of the track.
So, the distance traveled by A in the first meeting is (C - 100) meters.
The time taken by A to cover this distance is (C - 100) / vA seconds.
Similarly, the time taken by B to cover the 100 meters is 100 / vB seconds.
Second Meeting:
In the second meeting, B has traveled 60 meters before A completes one lap. This means B has covered (C - 60) meters in total.
The time taken by A to complete one lap is C / vA seconds.
Similarly, the time taken by B to cover (C - 60) meters is (C - 60) / vB seconds.
Since both meetings happened at the same time, we can equate the time taken by A and B in both cases.
(C - 100) / vA = 100 / vB --------(1)
C / vA = (C - 60) / vB --------(2)
Simplifying equation (1), we get:
CvB - 100vA = 100vB --------(3)
Simplifying equation (2), we get:
CvB = CvA - 60vB --------(4)
Adding equations (3) and (4), we get:
CvB + CvB = 100vB + CvA - 60vB
2CvB = CvA + 40vB
2C = C + 40
C = 40
Therefore, the circumference of the track is 40 meters. Hence, the correct answer is option 'D'.
First Meeting:
In the first meeting, B has traveled 100 meters. Since they are moving in opposite directions, the total distance covered by A and B together is equal to the circumference of the track.
So, the distance traveled by A in the first meeting is (C - 100) meters.
The time taken by A to cover this distance is (C - 100) / vA seconds.
Similarly, the time taken by B to cover the 100 meters is 100 / vB seconds.
Second Meeting:
In the second meeting, B has traveled 60 meters before A completes one lap. This means B has covered (C - 60) meters in total.
The time taken by A to complete one lap is C / vA seconds.
Similarly, the time taken by B to cover (C - 60) meters is (C - 60) / vB seconds.
Since both meetings happened at the same time, we can equate the time taken by A and B in both cases.
(C - 100) / vA = 100 / vB --------(1)
C / vA = (C - 60) / vB --------(2)
Simplifying equation (1), we get:
CvB - 100vA = 100vB --------(3)
Simplifying equation (2), we get:
CvB = CvA - 60vB --------(4)
Adding equations (3) and (4), we get:
CvB + CvB = 100vB + CvA - 60vB
2CvB = CvA + 40vB
2C = C + 40
C = 40
Therefore, the circumference of the track is 40 meters. Hence, the correct answer is option 'D'.
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Community Answer
A and B travel around a circular track at uniform speeds in opposite ...
Let x and y be the speed of A and B respectively and r be the radius of the circular track
If B has travelled 100m before they meet for first time, in the same time A would have travelled a distance of [ since they are starting at diametrically opposite points]. Hence,
And before meeting second time, A would have travelled a distance of 2r−60. Hence,
Answer is (D).
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A and B travel around a circular track at uniform speeds in opposite directions starting from diametrically opposite points. If they start at the same time, meet first after B has travelled 100 m and meet a second time 60 m before A completes one lap, then the circumference of the track in metres isa)400b)440c)420d)480Correct answer is option 'D'. Can you explain this answer?
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