Two persons A and B are standing diametrically opposite

Question

Two persons A and B are standing diametrically opposite on a circular track of with a radius of 3.5 units. They start running in an opposite direction on the circular track and their speeds are four units/min and seven units/min, respectively. On meeting each other, they take rest for half a min and then start running with twice the original speed. In five min, how many times will they take rest together?

A. 6
B. 7
C. 4
D. 5
E. 9

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A. 6
B. 7
C. 4
D. 5
E. 9

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Kinshook · Answer

Given: 
1. Two persons A and B are standing diametrically opposite on a circular track of with a radius of 3.5 units. 
2. They start running in an opposite direction on the circular track and their speeds are four units/min and seven units/min, respectively. 
3. On meeting each other, they take rest for half a min and then start running with twice the original speed.

Asked: In five min, how many times will they take rest together?

Their relative speed for the first round = 4 + 7 = 11 units / min
Distance to be covered for first meeting =  \pi *3.5 = 2* 22/7 * 3.5 = 11  units since they have to cover half of the circumference.
Distance to be covered in subsequent meetings = 22 units; Since they have to cover full circumference.
For subsequent meetings their relative speed doubles and time taken to cover the distance halves.
Time taken to meet for the first time = 11/11 = 1 mins
Time taken to meet for the second time = 22/22 = 1 mins
Time taken for meetings = {1,1,.5,.25,.125,,,,}

Meeting number  Travelling time  Rest Time  Total time  Cumulative Time  
  1  1 min  .5 min  1.5 min  1.5 min  
  2  1 min  .5 min  1.5 min  3 min  
  3  .5 min  .5 min  1 min  4 min  
  4  .25 min  .5 min  .75 min  4.75 min  
  5  .125 min      4.875 min

Since they meet for 5th time at 4.75 + .125 = 4.875 mins well within 5 mins time

IMO D

Kinshook · Answer

Hi  yashikaaggarwal 
What is the meaning of original speed in the question?
Is the speed doubles every time they meet or just once?

yashikaaggarwal · Answer

Original speed mean the speed they started running at opposite direction initially. I.e. 7&4 units respectively, will double after their first meet. 
Also, 
They will double their speed every time they meet each other after resting.

yashikaaggarwal · Answer

Answer is D, steps are similar to what Kinshook solved, the trick is the fifth rest starts just before the end of 5 minutes or 0.125 minutes precisely before 5th min end. So they took total rest for 5 times.

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Kinshook · Answer

Hi  yashikaaggarwal

Edited. Thanks

bumpbot · Answer

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Two persons A and B are standing diametrically opposite

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Meeting number	Travelling time	Rest Time	Total time	Cumulative Time
1	1 min	.5 min	1.5 min	1.5 min
2	1 min	.5 min	1.5 min	3 min
3	.5 min	.5 min	1 min	4 min
4	.25 min	.5 min	.75 min	4.75 min
5	.125 min			4.875 min

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Two persons A and B are standing diametrically opposite

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