Question

Candidates of four schools appear in a mathematics test. The data were as follows :

Schools	No. of candidates	Average Score
$I$	$60$	$75$
$II$	$48$	$80$
$III$	Not available	$55$
$IV$	$40$	$50$

If the average score of the candidates of all the four schools is $66,$ find the number of candidates that appeared from school $III$

Answer 1

Let $x$ be the number of candidates appeared from school $III$.

$\Rightarrow$ The average score of the candidates of all $4$ school $66$

$\Rightarrow$ $\frac{(60\times 75)+(48\times 80)+(x\times 55)+(40\times 50)}{60+48+x+40}=66$

$\Rightarrow$ $\frac{4500+3840+55x+2000}{148+x}=66$

$\Rightarrow$ $10340+55x=9768+66x$

$\Rightarrow$ $11x=572$

$\therefore$ $x=52$

$\therefore$ The number of candidates appeared from school $III$ are $52$