In a Mathematics test, the average marks of boys is `x%` and the average marks of girls is `y%` with `xney.` If the average marks of all students is `z%` the ration of the number of girls to the total number of students is

Options

A. `(z-x)/(y-x)`
B. `(z-y)/(y-x)`
C. `(z+y)/(y-x)`
D. `(z+x)/(y-x)`

Answer

A

Explanation

Given
Let no. of Boys = B `&` no of girls = G
`therefore` Sum of marks obtained by boys = b.x
`therefore` Sum of marks obtained by girls = Gy
Now, given
`(Bx+Gy)/(B+G)=z`
`B(x-z)=G(z-y)`
`(B)/(G)=(z-y)/(x-z)`
`"Add " 1`
`(B)/(G)+1=(z-y)/(x-z)+1`
`rArr(B+G)/(G)=(x-y)/(x-z)`
`rArr(G)/(B+G)=(z-x)/(y-x)`