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The average salary, per head, of all the workers of an institution is $Rs.\, 60 .$ The average salary of $12$ officers is $Rs.\, 400$; the average salary, per head, of the rest is $Rs.\,56.$ The total number of workers in the institution is
$1020$
$1032$
$1030$
$1035$
Solution
Let the total number of members in the institute be $Z$.
Average $=\frac{\text { sum }}{\text { number of elements }}$
Average salary of institution $=Rs.\, 60$.
Total salary of institution $=Rs.\, 60 Z$ Out of $Z$ persons, there are $12$ officers and then average salary is $=Rs.\, 400$
and so total salary of $12$ officers $=12 \times 400=Rs.\, 4800$. So, total salary of other $(z-12)$ members $=$ $₹(16 z-4800)$ …..$(1)$
Given that average salary of $(z-12)$ persons $=Rs.\, 56$ Here the total salary of $(z-12)$ people $=Rs.\, 56$ $(z-12)$ …..$(2)$
Equation $(1)$ and $(2)$ are equal $60=-4800=60 z-672$
$4 z=4128$
$z=1032$
