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15 children are given tags numbered from 1 to 15

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15 children are given tags numbered from 1 to 15  [#permalink]

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New post 05 Mar 2018, 06:57
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15 children are given tags numbered from 1 to 15 and are seated in a circular formation in the increasing order of their respective tag numbers. The total area covered by the circular formation is 36π square units and the distance between any two neighbouring children in the formation is equal. If the number of children seated between the child with tag number m and the child with tag number 1 is equal to the number of children seated between the child with tag number m and the child with tag number 15. what is the minimum distance covered along the circular formation by the child with tag number 1 to reach the child with tag number (m-2) and then go back to his original position?

(A) 4π

(B) 6π

(C) 8π

(D) 12π

(E) 16π

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Re: 15 children are given tags numbered from 1 to 15  [#permalink]

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New post 05 Mar 2018, 07:12
itisSheldon wrote:
15 children are given tags numbered from 1 to 15 and are seated in a circular formation in the increasing order of their respective tag numbers. The total area covered by the circular formation is 36π square units and the distance between any two neighbouring children in the formation is equal. If the number of children seated between the child with tag number m and the child with tag number 1 is equal to the number of children seated between the child with tag number m and the child with tag number 15. what is the minimum distance covered along the circular formation by the child with tag number 1 to reach the child with tag number (m-2) and then go back to his original position?

(A) 4π

(B) 6π

(C) 8π

(D) 12π

(E) 16π



so 15 students sit around a table..
Area of table = 36π = 6^2*pi.... Radius = 6
so circumference = 2*pi*r = 12*pi

Now if m is sitting in centre of 1 and 15, m = \(\frac{1+15}{2}=8\) and therefore m-2=8-2=6..

If the boy has to move from 1 to 6 and then 6 to 1, he covers GAP between (6-1)*2=10 gaps....
Now 12 *pi = 15 gaps, so 10 gaps will be \(\frac{10}{15}*12*pi = 8pi\)

C

You can also talk of each gap as some degree from centre of table but would mean the same

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Re: 15 children are given tags numbered from 1 to 15 &nbs [#permalink] 05 Mar 2018, 07:12
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