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.

Answer 1

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.