In a Mathematics test, average marks of boys is x % and average marks of girls is y % with x ≠ y .

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1.Set Theory

hard

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

A

$\frac{z-x}{y-x}$

B

$\frac{z-y}{y-x}$

C

$\frac{z+y}{y-x}$

D

$\frac{z+x}{y-x}$

(KVPY-2017)

Solution

(a)

Let the number of boy $=B$ and number of girls $=G$

Sum of marks obtained by boys $=B x$

$\therefore$ Sum of marks obtained by girls $=G y$

Now, given

$\frac{B x+G y}{B+G}=z$

$\Rightarrow B(x-z)=G(z-y)=\frac{B}{G}=\frac{z-y}{x-z}$

Now, $\frac{G}{B+G}=\frac{1}{\frac{B}{G}+1}=\frac{1}{\frac{z-y}{x-z}+1}=\frac{x-z}{x-y}$

$\frac{G}{B+G}=\frac{z-x}{y-x}$

Standard 11

Mathematics

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