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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?

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Solution

The correct option is **C** 100

The formula to calculate the weighted average is,

Weighted Average=(w1×n1)+(w2×n2)+…+(wl×nl)w1+w2+…+wl,

where w1,w2,…wl are the weighted factors and n1,n2,…nl 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 w1=25 and w2=x−25 and their corresponding average salaries are the data points represented as n1=800 and n2=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.

Weighted average salary=(w1×n1)+(w2×n2)w1+w2500=(25×800)+(x−25)400x500x=20000+400x−10000500x−400x=10000100x=10000x=10000100x=100

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

So, option (c) is correct.

The formula to calculate the weighted average is,

Weighted Average=(w1×n1)+(w2×n2)+…+(wl×nl)w1+w2+…+wl,

where w1,w2,…wl are the weighted factors and n1,n2,…nl 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 w1=25 and w2=x−25 and their corresponding average salaries are the data points represented as n1=800 and n2=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.

Weighted average salary=(w1×n1)+(w2×n2)w1+w2500=(25×800)+(x−25)400x500x=20000+400x−10000500x−400x=10000100x=10000x=10000100x=100

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

So, option (c) is correct.

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