Question

In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the non-manufacturing employees is

• A. 6 : 5
• B. 4 : 5
• C. 5 : 4
• D. 5 : 6

Answer 1

The Correct Option is B

Average Salary Calculation in Manufacturing and Non-Manufacturing Departments

We are given that the total number of employees in the organization is \(100x\), and each employee's wage is \(100y\). Let's analyze the situation step by step: 

Step 1: Manufacturing Department

The manufacturing department employs 20% of the total workforce. Therefore, the number of employees in the manufacturing department is \(20x\). Additionally, the combined salary of all manufacturing staff members is one-sixth of the total salary received by all employees.

The combined salary of the manufacturing department is:

\(\frac{1}{6} \times 100x \times 100y = \frac{10000xy}{6}\)

The average salary in the manufacturing department is then:

\(\frac{\frac{10000xy}{6}}{20x} = \frac{500y}{6x}\)

Step 2: Non-Manufacturing Department

The non-manufacturing department employs the remaining 80% of the workforce, meaning there are \(80x\) employees in the non-manufacturing department. The combined salary of the non-manufacturing department is:

\(\frac{50000xy}{6}\)

The average salary in the non-manufacturing department is:

\(\frac{\frac{50000xy}{6}}{80x} = \frac{500y}{24x}\)

Step 3: Ratio of Average Salaries

We now calculate the ratio of the average salary in the manufacturing department to the average salary in the non-manufacturing department:

\(\frac{\frac{500y}{6x}}{\frac{500y}{24x}} = \frac{500y}{6x} \times \frac{24x}{500y} = \frac{24}{6} = 4:15\)

Conclusion

Thus, the ratio of the average salary in the manufacturing department to the average salary in the non-manufacturing department is 4:15.

Therefore, the correct choice is (B): 4:15.