CAT 2025

Slot 3

QA

Question & SolutionQues & Sol

The average salary of 5 managers and 25 engineers in a company is 60000 rupees. If each of the managers received 20% salary increase while the salary of the engineers remained unchanged, the average salary of all 30 employees would have increased by 5%. The average salary, in rupees, of the engineers is

1. Concept Used

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

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 $(1)$:

$5(90000) + 25y = 1800000$

$450000 + 25y = 1800000$

$25y = 1350000$

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

3. Solution

Answer = Option C ✅

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