Question

The average salary of the school staff in a school is 4800 per month. The average salary of teachers is 8000 and that of non-teachers is 4000. If the number of
teachers are 6, then find the number of non-teachers in the
school?

a) 8
b) 12
c) 15
d) 5
e) None of these
​

Answer 1

Let :

Number of non-teacher = n

Given :

• Average salary of school staff = 4800
• Average salary of teachers = 8000
• Average salary of non-teacher = 4000
• Number of teachers = 6

Formula used :

Mean = Sum of observation ÷ Number of observation

Solution :

✪ Average salary of school staff = { ( Average salary of teachers × Number of teachers ) + (Average salary of non-teacher × Number of non-teacher) } ÷ (Number of teachers + Number of non-teacher)

$\sf \implies \: 4800 = \dfrac{(8000 \times 6) + (4000 \times n)}{(6 + n)} \\ \\ \sf \implies \: 4800(6 + n) = 48000 + 4000n \\ \\ \sf \implies \: 28800 + 4800n \: = \: 48000 + 4000n \\ \\ \sf \implies \: 4800n \: - 4000n \: = 48000 - 28800 \\ \\ \sf \implies \: 800n \: = \: 19200 \\ \\ \sf \implies \: n \: = \: \dfrac{19200}{800} \\ \\ \sf \implies \bold{n \: = \:24 }$

ANSWER :

Number of non-teacher = 24

e) None of these