Brain Teasers
Student Averages ...
Fun: 


(2.15)
Difficulty: 


(2.86)
Puzzle ID: #19274
Submitted By: lesternoronha1



Corrected By: MarcM1098








Submitted By: lesternoronha1





The average marks of girls in a class is equal to the number of boys and the average marks of boys in a class is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, find the minimum double digit number of students in the class.
Answer
The minimum double digit strength of the class is 18.Let the number of girls in the class be X and the number of boys in the class be Y.
Then the average marks of the girls and boys is Y and X respectively.
Class average
= (Total marks/Total number of students)
= (Total marks scored by girls and boys/Total number of students in the class)
= ((Y*X + X*Y)/(Y+X))
= ((2*X*Y)/(X+Y))
The average of the boys' average and the girls' average
= (X+Y)/2
It is given that the class average is 4 less than the average of the boys' average marks and the girls' average marks.
Hence
(X+Y)/2 - ((2*X*Y)/(X+Y)) = 4
Multiplying the above equation throughout by 2*(X+Y), we get
(X+Y)^2 - 4*X*Y = 8*(X+Y)
X^2 + Y^2 + 2*X*Y - 4*X*Y = 8*(X+Y)
X^2 + Y^2 - 2*X*Y = 8*(X+Y)
(X-Y)^2 = 8*(X+Y)
In order for the Right Hand Side in the above equation to be a perfect square, the value of (X+Y) should be of the type 2k^2 i.e. 2, 8, 18, 32, 50, 72 etc.
It is given that the minimum double digit strength of the class has to be found.
Therefore the minimum double digit strength of the class = X+Y = 18.
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