CAT 2023

Slot 2

QA

Question & Solution

1. Concept Used

• Topic: Ratio and Proportion — Average Salary Comparison
• Formula: $$\text{Average Salary} = \frac{\text{Total Salary}}{\text{Number of Employees}}$$

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2. Calculation

Let the total number of employees in the company be $100$ and the total salary of all employees be $S$.

Manufacturing Department:

Number of manufacturing employees $= 20%$ of $100 = 20$

Total salary of manufacturing employees $= \dfrac{S}{6}$ (given as one-sixth of total)

Average salary of manufacturing employees: $$\text{Avg}_{\text{mfg}} = \frac{S/6}{20} = \frac{S}{120}$$

Non-Manufacturing Department:

Number of non-manufacturing employees $= 100 - 20 = 80$

Total salary of non-manufacturing employees $= S - \dfrac{S}{6} = \dfrac{5S}{6}$

Average salary of non-manufacturing employees: $$\text{Avg}_{\text{non-mfg}} = \frac{5S/6}{80} = \frac{5S}{480} = \frac{S}{96}$$

Required Ratio: $$\frac{\text{Avg}{\text{mfg}}}{\text{Avg}{\text{non-mfg}}} = \frac{S/120}{S/96} = \frac{S}{120} \times \frac{96}{S} = \frac{96}{120} = \frac{4}{5}$$

So the ratio of average salary of manufacturing to non-manufacturing employees is $4 : 5$.

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3. Solution

Answer = Option B ✅

The ratio of the average salary of manufacturing employees to non-manufacturing employees is 4 : 5.