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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 |
| 1 | 60 | 75 |
| 2 | 48 | 80 |
| 3 | N A | 55 |
| 4 | 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 3.
Solution
Let no. of candidates appeared from school 3 = x.
| Schools | No.of candidates |
Average score |
| 1 | 60 | 75 |
| 2 | 48 | 80 |
| 3 | x | 55 |
| 4 | 40 | 50 |
Given, average score of all school = 66.
⇒ `(N_1barx_1 +N_2barx_2 + N_3barx_3 + N_4barx_4 )/(N_1 +N_2 + N_3 + N _4) = 66`
⇒ `(60+ 75 + 48 +80 + x xx 55 +40 xx 50)/(60 + 48 + x +40)= 66`
⇒`(4500 + 3840 + 55x + 2000)/148 + x`
⇒`(10340 + 55x)/(148 + x) = 66`
⇒ 10340 + 55x = 66x + 9768
⇒ 10340 + 9768 = 66x - 55x
⇒ 11x = 572
⇒ `x = 572/11`= 52
∴ No. of candidates appeared from school (3) – 52.
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