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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 | NA | 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.
Solution
Let the number of candidates from school III = P
| Schools |
No. of Candidates (N1) |
Average scores (x1) |
| I | 60 | 75 |
| II | 48 | 80 |
| III | P | 55 |
| IV | 40 | 50 |
Given
Average score or all schools = 66
`rArr(N_1barx_1+N_2barx_2+N_3barx_3+N_4barx_4)/(N_1+N_2+N_3+N_4)=66`
`rArr(60xx75+48xx80+Pxx55+40xx50)/(60+48+P+40)=66`
`rArr(4500+3840+55P+2000)/(148+P)=66`
⇒ 4500 + 3840 + 55P + 2000 = 66(148 + P)
⇒ 10340 + 55P = 66P + 9768
⇒ 10340 - 9768 = 66P - 55P
⇒ 572 = 11P
`rArrP=572/11`
⇒ P = 52
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