CAT 2025

Slot 3

QA

Question & Solution

1. Concept Used

• Topic: Averages & Linear Equations
• Formula: $$\text{Total Salary} = \text{Number of Employees} \times \text{Average Salary}$$

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2. Calculation

Let the average salary of the 5 managers be $$x$$ and the average salary of the 25 engineers be $$y$$.

The total number of employees is $$5 + 25 = 30$$, and the overall average salary is $$60000$$. So the total salary is:

$$30 \times 60000 = 1800000$$

This gives us our first equation:

$$5x + 25y = 1800000 \quad \cdots (1)$$

Now, the average salary of all 30 employees increases by $$5%$$. Since the number of employees remains the same, the total salary also increases by $$5%$$:

$$\text{New Total} = 1800000 \times 1.05 = 1890000$$

Only the managers receive a $$20%$$ salary hike, so their new average becomes $$1.2x$$. The engineers' salaries are unchanged at $$y$$. This gives us the second equation:

$$5 \times 1.2x + 25y = 1890000$$

$$6x + 25y = 1890000 \quad \cdots (2)$$

Subtracting equation $$(1)$$ from equation $$(2)$$:

$$(6x + 25y) - (5x + 25y) = 1890000 - 1800000$$

$$x = 90000$$

Substituting $$x = 90000$$ back into equation $$(1)$$:

$$5(90000) + 25y = 1800000$$

$$450000 + 25y = 1800000$$

$$25y = 1350000$$

$$y = \frac{1350000}{25} = 54000$$

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3. Solution

Answer = Option C ✅

The average salary of the engineers is ₹54,000.