Question

The average salary of all the workers in a workshop is ₹11500.
If the average salary of 5 technicians is ₹8000 and the average salary of the rest of the workers is ₹14000, then the total number of workers in the workshop is

• A. 11
• B. 12
• C. 13
• D. 14

Answer 1

The correct option is B 12

Let:
T = Total number of workers
$S_T$ = Sum of salaries of T workers
$S_5$ = Sum of salaries of 5 workers
Average of numbers = $\frac{\text{Sum of numbers}}{\text{Total number of numbers}}$
∴ 11500 = $\frac{\text{Sum of total salary of workers}}{\text{Total number of workers}}$
$\Rightarrow 11500=\frac{S_T}{T}$
$\Rightarrow S_T=11500\times T$ .........(i)
and $8000=\frac{\text{Sum of salary of 5 workers}}{5}$
$\Rightarrow S_5=8000\times 5$
$\Rightarrow S_5=40000$ …..(ii)
and, $14000=\frac{\text{Sum of (T-5) workers}}{\text{(T-5)workers}}$
$\Rightarrow S_T–S_5=14000\times (T–5)$ …..(iii) Substituting the values of (i) and (ii) in (iii), we get
$\Rightarrow 11500\times T-40000=14000\times (T-5)$
$\Rightarrow 115T–400=140T–700$
$\Rightarrow 700–400=140T–115T$
$\Rightarrow 300=25T$
$\Rightarrow T=12$
Therefore, there are total of 12 workers in the workshop.
Hence, the correct answer is option (b).