CAT 2025 Slot3 Quant: The average salary of 5 managers and 25 engineers in a company is 60000 rupees

Step 1: Calculate the total increase in salary pool
Number of employees = $30$. Original average = $60,000$.
Increase in average = $5\%$ of $60,000 = 3,000$.
Total increase in salary = $30 \times 3,000 = 90,000$.

Step 2: Find the average salary of a manager (M)
The increase only comes from managers. Let $M$ be the manager's average salary.
Increase $= 20\% \text{ of } (5 \times M) = 90,000$
$0.2 \times 5 \times M = 90,000 \implies 1 \times M = 90,000$.
The average salary of a manager is $90,000$.

Step 3: Solve for the engineer's average salary (E)
Total Salary $= (5 \times 90,000) + (25 \times E) = 30 \times 60,000$
$450,000 + 25E = 1,800,000$
$25E = 1,350,000$
$E = \frac{1,350,000}{25} = \mathbf{54,000}$.