Question

In a company, the weighted average salary of the employees is $\$500$. The average salary of $25$ employees is $\$800$, while the average salary of the remaining employees is $\$600$. What is the total number of employees in the company?

• A. $25$
• B. $50$
• C. $100$
• D. $125$

Answer 1

The correct option is C $100$

The formula to calculate the weighted average is,

$\text{Weighted Average}=\frac{(w_1\times n_1)+(w_2\times n_2)+\dots +(w_l\times n_l)}{w_1+w_2+\dots +w_l}$,

where $w_1,w_2,\dots w_l$ are the weighted factors and $n_1,n_2,\dots n_l$ are the data points.

Let the total number of employees in the company be $x$.

Then, the given information can be represented in the tabular form as,


Here, the weighted factors are the number of employees, denoted by $w_1=25$ and $w_2=x-25$ and their corresponding average salaries are the data points represented as $n_1=800$ and $n_2=400$.

It is given that the weighted average salary of the employes is $\$500$.

Thus, substitute the values of weighted factors, data points, and the weighted average salary in the formula of weighted salary to calculate the value of $x$.

$\begin{array}{cc}\text{Weighted average salary}& =\frac{(w_1\times n_1)+(w_2\times n_2)}{w_1+w_2}\\ 500& =\frac{(25\times 800)+(x-25)400}{x}\\ 500x& =20000+400x-10000\\ 500x-400x& =10000\\ 100x& =10000\\ x& =\frac{10000}{100}\\ x& =100\end{array}$

Hence, the total number of employees in the company is $100$.

So, option (c) is correct.