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

Calculation of Average Salaries in Manufacturing and Non-Manufacturing Departments

Given a total of \(100x\) employees, with each earning \(100y\), we proceed with the analysis.

Step 1: Manufacturing Department

This department comprises 20% of the total employees, equating to \(20x\) individuals. Their collective salary is one-sixth of the organization's total payroll.

Total salary for the manufacturing department:

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

Average salary in the manufacturing department:

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

Step 2: Non-Manufacturing Department

The non-manufacturing department accounts for the remaining 80% of the workforce, comprising \(80x\) employees. Their combined salary is:

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

Average salary in the non-manufacturing department:

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

Step 3: Ratio of Average Salaries

The ratio of the average salary in the manufacturing department to that in the non-manufacturing department is calculated as follows:

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

Conclusion

The ratio of the average salary in the manufacturing department to the average salary in the non-manufacturing department is determined to be 4:15.

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