Question

The average salary of all the workers in a workshop is Rs. $8000$. The average salary of $7$ technicians is Rs. $12000$ and the average salary of the rest is Rs. $6000$. The total number of workers in the workshop are

• A. 20
• B. 21
• C. 22
• D. 23

Answer 1

The correct option is B 21

Let the number of workers be $x$

Given that the average salary of $7$ workers is Rs. $12000$

Therefore, $12000=\frac{\text{sum of the salaries of 7 workers}}{7}$

$\text{sum of the salaries of 7 workers}=84000$ ------(1)

The remaining number of workers is $x-7$

Given that average salary of the remaining workers is Rs. $6000$

Therefore, $6000=\frac{\text{sum of the salaries of (x-7) workers}}{x-7}$

$\text{sum of the salaries of (x-7) workers}=6000x-42000$ ------(2)

Given that the average salary of all the workers is Rs. $8000$

Therefore, $8000=\frac{\text{sum of the salaries of 7 workers + sum of the salaries of (x-7) workers}}{x}$ -----(3)

substituting (1) and (2) in (3) we get

$8000x=84000+6000x-42000$

$⟹8000x-6000x=84000-42000$

$⟹2000x=42000$

$⟹x=21$

Therefore, the total number of workers in the workshop is $21$