Question

Candidates of 5 schools appear in a maths test. The data is given as follows :

$\begin{array}{ccc}\text{Schools}& \text{No.of Candidates}& \text{Score}\\ A& 60& 75\\ B& 48& 80\\ C& -& 55\\ D& 40& 50\\ E& 50& 60\end{array}$

If the average score of the candidates is 64.8, then find the number of candidates from school C.

Answer 1

Let the number of candidates from School C be $x$

Mean $=\frac{\sum No.ofcandidates\times Score}{\sum TotalNo.ofCandidates}$

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

$=\frac{4500+3840+55x+2000+3000}{198+x}$

$=\frac{13340+55x}{198+x}$

Given, mean = 64.8

$\therefore$ We get

$\frac{13340+55x}{198+x}=64.8$

$\Rightarrow 13340+55x=12830.4+64.8x$

$\Rightarrow 9.8x=509.6$

$\Rightarrow x=\frac{509.6}{9.8}=52$

Hence the number of candidates from School C = 52.