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1.Set Theory
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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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