KVPY SA Exam 19-Nov-2017 Question Paper

Question : 15 of 80

Marks: +1, -0

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

${z- x}/{y-x}$
${z-y}/{y-x}$
${z- y}/{y-x}$
${z+ x}/{y-x}$

Validate

Solution:

Given
Let no. of Boys = B & no of girls = G
∴ Sum of marks obtained by boys = B.x
∴ Sum of marks obtained by girls = G.y
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

⇒ {B+G}/G={x-y}/{x-z}

⇒

G/{B+G}={z-x}/{y-x }

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