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Three friends A, B and C decide to run around a circular track.

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Three friends A, B and C decide to run around a circular track.  [#permalink]

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New post 05 May 2019, 20:27
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A
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Three friends A, B, and C decide to run around a circular track. They start at the same time and run in the same direction. A is the quickest and when A finishes a lap, it is seen that C is as much behind B as B is behind A. When A completes 3 laps, C is the exact same position on the circular track as B was when A finished 1 lap. Find the ratio of the speeds of A, B, and C?

A. 5 : 4 : 2
B. 4 : 3 : 2
C. 5 : 4 : 3
D. 3 : 2 : 1
E. 5 : 3 : 1

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Three friends A, B and C decide to run around a circular track.  [#permalink]

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New post 05 May 2019, 21:09
1
Let the length of track is 'L'
When A finished lap 1, assume B is at L-x and C at L-2x
When A finished 3rd track, C must be at L-x or 2L-x (In both scenario he is at same position, as B was when A finished 1st lap)
Case 1
If C is in lap 1, when A finished his 3rd lap
3*(L-2x)= L-x
3L-6x=L-x
2L=5x
A:B:C=L:(L-x):(L-2x)
A:B:C=L : (L-{2L/5}) : (L-{4L/5}) = L : 3L/5 : L/5
A:B:C= 5:3:1

Case 2
If C is in lap 2, when A finished his 3rd lap
3*(L-2x)= 2L-x
3L-6x=2L-x
L=5x
A:B:C=L:(L-x):(L-2x)
A:B:C=L : (L-{L/5}) : (L-{2L/5}) = L : 4L/5 : 3L/5
A:B:C= 5:4:3

C and E both can be correct
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Re: Three friends A, B and C decide to run around a circular track.  [#permalink]

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New post 06 May 2019, 04:26
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DisciplinedPrep wrote:
Three friends A, B, and C decide to run around a circular track. They start at the same time and run in the same direction. A is the quickest and when A finishes a lap, it is seen that C is as much behind B as B is behind A. When A completes 3 laps, C is the exact same position on the circular track as B was when A finished 1 lap. Find the ratio of the speeds of A, B, and C?

A. 5 : 4 : 2
B. 4 : 3 : 2
C. 5 : 4 : 3
D. 3 : 2 : 1
E. 5 : 3 : 1


Think about the distance covered by each individual at a point of time and anchor the question around it.

Let track length be equal to T. When A completes a lap, let us assume B has run a distance of (t - d). At this time, C should have run a distance of (t - 2d).

After 3 laps C is in the same position as B was at the end of one lap. So, the position after 3t - 6d should be the same as t - d. Or, C should be at a distance of d from the end of the lap. C will have completed less than 3 laps (as he is slower than A), so he could have traveled a distance of either t - d or 2t - d.

=> 3t - 6d = t - d
=> 2t = 5d
=> d = 0.4t

The distances covered by A, B and C when A completes a lap will be t, 0.6t and 0.2t respectively. Or, the ratio of their speeds is 5 : 3 : 1.

In the second scenario, 3t - 6d = 2t - d => t = 5d => d = 0.2t.

The distances covered by A, B and C when A completes a lap will be t, 0.8t and 0.6t respectively. Or, the ratio of their speeds is 5 : 4 : 3.

The question is " Find the ratio of the speeds of A, B and C?"
The ratio of the speeds of A, B and C is either 5 : 3 : 1 or 5 : 4 : 3.
Hence, the answer is 5 : 4 : 3

Choice C is the correct answer.
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Re: Three friends A, B and C decide to run around a circular track.   [#permalink] 06 May 2019, 04:26
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Three friends A, B and C decide to run around a circular track.

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