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 36 square units and the distance between any two neighbouring children in the formation is equal., If thenumber of children seated between the child with tag number m and the child with tag number 1is 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)4b)6c)8d)12e)16Correct answer is option 'C'. Can you explain this answer?

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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

Correct answer is option 'C'. Can you explain this answer?

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15 children are given tags numbered from 1 to 15 and are seated in a c...

Given

15 children are seated at equal distance in a circular formation
- Let the distance between two neighboring students be x.

Area of the circular formation = 36π
- Let’s assume the radius of the circular formation be r
- πr²=36π

Child number ‘m’ is equidistant from child number 1 and child number 15

To Find:

Minimum distance covered by child number 1 to reach child number m -2 and back to his original position

Approach

Let’s understand first how we can find the distance between any two children.
- Let’s assume we need to find the distance between child number 1 and child number 4.
- As the distance between two neighboring children is x, distance between child number 4 and child number 1 will be
  1. Case 1: Distance =(4-1) * x = 3x
  2. Case 2: Distance = 15x – 3x = 12x
    1. 15x is the total distance along the circular formation for 15 children.
  3. So minimum distance will be = minimum {distance a, distance b} = minimum {3x,12x} = 3x
- So based on the example above we can infer that in general the minimum distance between any two children = Minimum {distance c, distance d}, where
  1. distance c = ((Position of first child – Position of second child))*x
  2. distance d = 15x – ((Position of first child – Position of second child))*x
- Now, distance c & distance d or any distance between children is a part of the perimeter of the circle.
  1. So, we can write 15x = 2πr
- Thus, if we know the value of r, we can find the value of x.
Hence, for finding the distance traveled, we need to find the following:
1. Value of m
2. Radius of the circle i.e. r
Value of m
1. As child m is equidistant from child number 1 and child number 15, we can write
  1. Distance between child number m and child number 1 = Distance between child number 15 and child number m
  2. (m-1)*x = (15-m)*x
  3. This will give us the value of m and hence we can find the value of m -2
Radius of the circle
1. We know that πr2=36π
2. We can use the above equation to find out the value of r.

Working Out

Finding value of m
- (m – 1)*x = (15- m)*x, i.e. m = 8
- Hence, m – 2 = 6
Calculating minimum distance
- distance c = ((position of child number m - 2 ) – (position of child number 1))*x
- So, distance c = (6-1)*x = 5x
- distance d = 15x - ((position of child number m - 2 ) – (position of child number 1))*x
- So, distance d = 15x – 5x
- Minimum distance = minimum {distance c, distance d}
  - So, minimum distance = minimum {5x,10x} = 5x
  - Distance to go back to original position = 5x+5x =10x

Therefore, the correct answer is Option C.

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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 thenumber of children seated between the child with tag number m and the child with tag number 1is 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)4πb)6πc)8πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer?

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