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The average score of boys in an examination of a school is $71$ and that of girls is $73.$ The average score of the school in that examination is $71.8$. Find the ratio of the number of boys to the number of girls that appeared in the examination :

  1. $2: 2$
  2. $4: 2$
  3. $3: 2$
  4. $1: 2$
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let $x$ is the number of boys, $y$ is the number of girls.

average score of boys $(A)=71$

average score of girls $(B)=73$

The average score of the school= $\frac{A*x+B*y}{x+y}$

$\implies 71.8=\frac{71*x+73*y}{x+y}$

$\implies71.8x+71.8y=71x+73y$

$\implies x(71.8-71)=y(73-71.8)$

$\implies 0.8x=1.2y$

$\implies x:y=3:2$

Option $(C)$ is correct.

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