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Salary Ratio

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Salary Ratio


1. **Problem Statement:** We are given that 20% of employees work in manufacturing, and the total salary of manufacturing employees is one-sixth of the total salary of all employees. We need to find the ratio of average salary of manufacturing employees to that of non-manufacturing employees. 2. **Define variables:** Let total number of employees be $N$. Manufacturing employees = $0.20N$, non-manufacturing employees = $0.80N$. Let total salary of all employees = $S$. Given manufacturing employees total salary = $\frac{1}{6}S$, so non-manufacturing total salary = $S - \frac{1}{6}S = \frac{5}{6}S$. 3. **Calculate average salaries:** Average salary of manufacturing employees = $\frac{\text{total manufacturing salary}}{\text{number of manufacturing employees}} = \frac{\frac{1}{6}S}{0.20N} = \frac{\frac{1}{6}S}{\frac{1}{5}N} = \frac{1}{6}S \times \frac{5}{1N} = \frac{5S}{6N}$. Average salary of non-manufacturing employees = $\frac{\frac{5}{6}S}{0.80N} = \frac{\frac{5}{6}S}{\frac{4}{5}N} = \frac{5}{6}S \times \frac{5}{4N} = \frac{25S}{24N}$. 4. **Find the ratio:** $$ \text{Ratio} = \frac{\text{average manufacturing salary}}{\text{average non-manufacturing salary}} = \frac{\frac{5S}{6N}}{\frac{25S}{24N}} = \frac{5S}{6N} \times \frac{24N}{25S} = \frac{5 \times 24}{6 \times 25} = \frac{120}{150} = \frac{4}{5} $$ 5. **Conclusion:** The ratio of the average salary of manufacturing employees to non-manufacturing employees is $4:5$. **Answer: B) 4:5**