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Question

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

SchoolsNo.of CandidatesAverage ScoreI6075II4880IIINot Available55IV4050

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

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B

52

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C

49

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D

51

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Solution

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

Total score=(148+p)×66

Now mean score of 60 candidates in school I=75 Total=60×75=4500In school II,mean of 48 candidates=80 Total=48×80=3840In school III,mean of p candidates=55 Total=55×p=55pIn school IV,mean of 40 candidates=50 Total=40×50=2000Now total number of candidates of 4 schools=148+p and total score =4500+3840+55p+2000=10340+55p 10340+55p=(148+p)×66=9768+66p103409768=66p55p572=11p p=57211=52 Number of candidates in school III=52


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