Question

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

$\begin{array}{ccc}Schools& No.ofCandidates& AverageScore\\ I& 60& 75\\ II& 48& 80\\ III& NotAvailable& 55\\ IV& 40& 50\end{array}$

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

$\therefore Totalscore=(148+p)\times 66$

$Nowmeanscoreof60candidatesinschoolI=75\therefore Total=60\times 75=4500InschoolII,meanof48candidates=80\therefore Total=48\times 80=3840InschoolIII,meanofpcandidates=55\therefore Total=55\times p=55pInschoolIV,meanof40candidates=50\therefore Total=40\times 50=2000Nowtotalnumberofcandidatesof4schools=148+pandtotalscore=4500+3840+55p+2000=10340+55p\therefore 10340+55p=(148+p)\times 66=9768+66p\Rightarrow 10340-9768=66p-55p\Rightarrow 572=11p\therefore p=\frac{572}{11}=52\therefore NumberofcandidatesinschoolIII=52$