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.

Answer 1

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

${\displaystyle \Rightarrow \frac{N_1{\overline{x}}_1+N_2{\overline{x}}_2+N_3{\overline{x}}_3+N_4{\overline{x}}_4}{N_1+N_2+N_3+N_4}=66}$

${\displaystyle \Rightarrow \frac{60\times 75+48\times 80+P\times 55+40\times 50}{60+48+P+40}=66}$

${\displaystyle \Rightarrow \frac{4500+3840+55P+2000}{148+P}=66}$

⇒ 4500 + 3840 + 55P + 2000 = 66(148 + P)

⇒ 10340 + 55P = 66P + 9768

⇒ 10340 - 9768 = 66P - 55P

⇒ 572 = 11P

${\displaystyle \Rightarrow P=\frac{572}{11}}$

⇒ P = 52