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30 Jun 2019, 09:54
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
56% (03:20) correct
44%
(02:50)
wrong
based on 90
sessions
History
Date
Time
Result
Not Attempted Yet
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) 4\(\pi\)
(B) 6\(\pi\)
(C) 8\(\pi\)
(D) 12\(\pi\)
(E) 18\(\pi\)
(A) 4\(\pi\)
(B) 6\(\pi\)
(C) 8\(\pi\)
(D) 12\(\pi\)
(E) 18\(\pi\)
30 Jun 2019, 10:23
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ArtyomYom
Solution
Given Area = 36p
15 children in equal distance between each other. They formate the circular.
Need to find the distance, that '1' boy must come to m-2, and come back to his place.
Approach
Answer = Distance to (m-2) * 2(to m-2 and back)
m=8 (median)
m-2 = 6
Insite:
we take 5 instead of 6, coz we need to calculate distance
1____2____3___4____5_____6
There are only 5 '___'
Distance to (m-2) = (length of the distance between 2 boys) * 5
length of the distance between 2 boys = Length of circular / 15(quantity of boys)
Length of the circular = 2pr
A = pr^2
36p = pr^2
r^2=36
r = 6
Length of the circular = 12p
length of the distance between 2 boys = (4/5)p
Distance to (m-2) = (5*4/5)*p
Answer = 8p
C
03 Jul 2019, 19:29
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A very verbose question and hence a lot of data to deal with. However, break the data into smaller parts and you’ll see that this is actually not all that difficult.
The area of the circle is 36π sq.units. From this, we can calculate the radius of the circle to be 6 units.
We also know that the distance between any two neighboring children in the formation is equal. This means that the circumference of the circle can be divided into 15 equal parts.
Since the radius of the circle is 6 units, the circumference of the circle is 12π units. Dividing this into 15 parts, each part is at a distance of 4π/5 units from each other.
The question says that person with tag number m is equidistant from the child with tag number 1 and tag number 15. This is to say that m is the median of the tag numbers.
Therefore, m = 8. So, m-2 = 6.
The distance between child with tag 1 and child with tag 5 = \(\frac{4π}{5}\) * 5 = 4π (because between child 1 and child 6, there are 5 parts each of length 4π/5 units).
The child with tag 1 has to traverse this distance twice. So, the total distance travelled by him is 8π.
The correct answer option is C.
Hope this helps!
The area of the circle is 36π sq.units. From this, we can calculate the radius of the circle to be 6 units.
We also know that the distance between any two neighboring children in the formation is equal. This means that the circumference of the circle can be divided into 15 equal parts.
Since the radius of the circle is 6 units, the circumference of the circle is 12π units. Dividing this into 15 parts, each part is at a distance of 4π/5 units from each other.
The question says that person with tag number m is equidistant from the child with tag number 1 and tag number 15. This is to say that m is the median of the tag numbers.
Therefore, m = 8. So, m-2 = 6.
The distance between child with tag 1 and child with tag 5 = \(\frac{4π}{5}\) * 5 = 4π (because between child 1 and child 6, there are 5 parts each of length 4π/5 units).
The child with tag 1 has to traverse this distance twice. So, the total distance travelled by him is 8π.
The correct answer option is C.
Hope this helps!
