Calculating New Average Salary

The problem states the new average salary is ₹ 4000/- more than that of the guard.

• Guard's Salary = ₹ 5000/-
• New Average Salary = Guard's Salary + ₹ 4000/-
• New Average Salary = ₹ 5000 + ₹ 4000 = ₹ 9000/-

Setting Up the Salary Equation

Let the initial number of staff be $n$.

• Initial Average Salary = ₹ 8000/-
• Initial Total Salary = $8000 \times n$
• Two new employees are added (guard and manager).
• New Staff Strength = $n + 2$
• Salaries of new employees = ₹ 5000 (guard) + ₹ 20000 (manager) = ₹ 25000
• New Total Salary = Initial Total Salary + Salaries of new employees
• New Total Salary = $8000n + 25000$
• The new average salary is calculated as:
$ \text{New Average Salary} = \frac{\text{New Total Salary}}{\text{New Staff Strength}} $

Solving for Initial Staff Strength

Substitute the known values into the average salary formula:

• $₹ 9000 = \frac{8000n + 25000}{n + 2}$
• Multiply both sides by $(n + 2)$:
$ 9000(n + 2) = 8000n + 25000 $
• Distribute and simplify:
$ 9000n + 18000 = 8000n + 25000 $
• Rearrange terms to solve for $n$:
$ 9000n - 8000n = 25000 - 18000 $ $ 1000n = 7000 $
• Calculate $n$:
$ n = \frac{7000}{1000} = 7 $
• This value, $n=7$, represents the initial staff strength.

Determining Current Staff Strength

The question asks for the *current* staff strength after the new recruits.

• Current Staff Strength = Initial Staff Strength ($n$) + Number of New Employees
• Current Staff Strength = $7 + 2 = 9$