UPSC 2016 CDS II Math Paper

Let the number of students in class X, Y and Z be x, y and z, respectively.
Total score of students in class X and Y = Total score of students in class X + Total score of students in class Y
⇒79(x+y)=83x+76y
⇒4x=3y
Total score of students in class Y and Z = Total score of students in class Y + Total score of students in class Z
⇒81(y+z)=76y+85z
⇒5y=4z
∴ 20x=15y=12z
Ratio of number of students in the class=

1

20

:

1

15

:

1

12

=3:4:5
∴ Average sore of X, Y and Z
=

83×3k+76×4k+85×5k

3k+4k+5k

=

978

12

=8.15