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# Two cyclists are running on a circular track of 500m...

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Two cyclists are running on a circular track of 500m...  [#permalink]

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13 Mar 2014, 03:37
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70% (01:39) correct 30% (02:29) wrong based on 180 sessions

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Two cyclists are running on a circular track of 500m.They start from the same point A at the same time.If they meet for the first time at a point 200 m from A, which of the following could be the possible ratio of their speeds?

A. 1:3
B. 2:3
C. 3:5
D. 5:7
E. 7:11

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Re: Two cyclists are running on a circular track of 500m...  [#permalink]

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13 Mar 2014, 04:43
First thing's first. Why are cyclists running?

Someone can correct me if I'm wrong, but I don't think the answer is among the solutions.

Basically, to meet at 200m from A, one person needs to run 200+500x meters, while the other person runs at 200+500y meters. So ratio of speeds needs to be something like 2/7, 7/12, 12/17, etc.

There is, however, another possibility of meeting at 300m from A (and since it's a circle, it's really still 200m from A). In this case, the ratio needs to be something like 3/8, 8/13, 13/18, etc.

1:3, cyclists will first meet at 250m from A (after traveling 750m)
2:3, cyclists will first meet at 0m from A (after traveling 1500m)
3:5, cyclists will first meet at 250m from A (after traveling 1250m)
5:7, cyclists will first meet at 250m from A (after traveling 1750m)
7:11, cyclists will first meet at 375m from A (after traveling 1375m)
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Re: Two cyclists are running on a circular track of 500m...  [#permalink]

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13 Mar 2014, 05:13
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The trick here is that it has not been mentioned anywhere about the direction in which they are running(Still couldn't figure out why they are running.. )..if we consider opposite directions then here is how it follows:
So starting from the point A when cyclist 1 has run 200m & cyclist 2 has run 300m. They will meet at a point 200 m from A and the ratio of their speeds will be proportionally 2:3..
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Re: Two cyclists are running on a circular track of 500m...  [#permalink]

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13 Mar 2014, 13:08
well, the key aspect of this question is the distance mentioned, when they met for the first time, which is 200m away from the starting point. This distance between their first meeting can be less than 500 in only two circumstance.

1) if both are travelling in the same direction and one of them has been given a head start say by few meters.

2) or if both are travelling in the opposite direction.

now since they start their journey at the same time. hence option 1 is ruled out. hence they must be running in the opposite direction. hence answer should be 2:3.
Why?? here is a solution
As here time is constant, therefore, distance traveled will be directly proportional to the the respective velocities/speed of the two runners.(d1/d2=v1/v2)
now one of them has covered 200m, therefore other must have covered 300m, therefore ratio of their speeds/velocities will be 2:3
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Re: Two cyclists are running on a circular track of 500m...  [#permalink]

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22 Apr 2015, 18:50
First: why are they running lol

Second: this would depend on whether they are running in the same direction as well (maybe one guy is running really fast and catches up to the other guy). But I assumed they ran in the opposite directions and my method was as so:

200m out of 500m = 40% of the track, so one person has gotten 40% while the other has gotten 60% ---> the ratio between these is 2:3
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Re: Two cyclists are running on a circular track of 500m...  [#permalink]

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03 Jul 2015, 05:37
JusTLucK04 wrote:
Two cyclists are running on a circular track of 500m.They start from the same point A at the same time.If they meet for the first time at a point 200 m from A, which of the following could be the possible ratio of their speeds?

A. 1:3
B. 2:3
C. 3:5
D. 5:7
E. 7:11

Yeah, very poor but funny question. Cyclists who are running, wow. Then there is no source.

If you solve it and assume that they both run/or cycle in opposite direction, there is no reason to calculate any speed. Just calculate the ratio: if they meet at a point 200m from A, one cyclist must have absolved 200m and the other 300m. Therefore 2:3
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Re: Two cyclists are running on a circular track of 500m...  [#permalink]

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20 Jan 2016, 06:39
JusTLucK04 wrote:
The trick here is that it has not been mentioned anywhere about the direction in which they are running(Still couldn't figure out why they are running.. )..if we consider opposite directions then here is how it follows:
So starting from the point A when cyclist 1 has run 200m & cyclist 2 has run 300m. They will meet at a point 200 m from A and the ratio of their speeds will be proportionally 2:3..

Thank you for explaining the tricky part. I was driving myself nuts, since I couldn't figure out, why it was so hard for me to answer such an easy question.
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Re: Two cyclists are running on a circular track of 500m...  [#permalink]

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28 Jul 2018, 03:41
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Re: Two cyclists are running on a circular track of 500m... &nbs [#permalink] 28 Jul 2018, 03:41
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