Question

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

$\begin{array}{ccc}\text{Schools}& \text{No. of Candidates}& \text{Average Score}\\ I& 60& 75\\ II& 48& 80\\ III& \text{Not Available}& 55\\ IV& 40& 50\end{array}$

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

• A. 50
• B. 52
• C. 49
• D. 51

Answer 1

The correct option is B

52

Let number of candidates in school III=p

Then total number of candidates in 4 schools =60+48+p+40=148+p

Average score of 4 schools=66

$\therefore$ Total score = (148+p) $\times$ 66

Now mean score of 60 candidates in school I=75
$\therefore$ Total = 60 $\times$ 75 =4500
In school II, mean of 48 candidates = 80
$\therefore$ Total = 48 $\times$ 80 = 3840
In school III, mean of p candidates = 55
$\therefore$ Total = 55 $\times$ p = 55p
In school IV, mean of 40 candidates = 50
$\therefore$ Total = 40 $\times$ 50 = 2000
Now total number of candidates of 4 schools = 148+p
and total score = 4500 + 3840 + 55p + 2000 = 10340 + 55p
$\therefore$ 10340 + 55p = (148+p) $\times$ 66 = 9768 + 66p
$\Rightarrow$ 10340 - 9768 = 66p - 55p
$\Rightarrow$ 572 = 11p
$\therefore$ p = $\frac{572}{11}$ = 52
$\therefore$ Number of candidates in school III = 52