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

The correct answer is 54000 (Option 3).

Let's solve this step-by-step to find the average salary of the engineers.

Step 1: Calculate the total initial salary of all employees.

The total number of employees is 5 managers + 25 engineers = 30 employees.

The average salary of these 30 employees is 60,000 rupees.

Therefore, the total initial salary of all 30 employees is:

$\text{Total Initial Salary}=30\times 60000=1800000\text{rupees}$

Step 2: Determine the total salary increase.

If each manager receives a 20% salary increase, the overall average salary of all 30 employees increases by 5%.

The total increase in salary across all employees is:

$\text{Total Increase}=5\%\text{of}1800000=\frac{5}{100}\times 1800000=90000\text{rupees}$

Step 3: Find the total initial salary of the managers.

Since only the managers received a salary increase, the entire increase of 90,000 rupees comes from the 20% increase in the managers' total salary.

Let M_total be the total initial salary of the 5 managers.

$20\%\text{of}{M}_{\text{total}}=90000$

$\frac{20}{100}\times M_{\text{total}}=90000$

$M_{\text{total}}=90000\times 5=450000\text{rupees}$

Step 4: Find the total initial salary of the engineers.

Subtract the total salary of the managers from the total salary of all 30 employees:

$\text{Total Engineers' Salary}=1800000-450000=1350000\text{rupees}$

Step 5: Calculate the average salary of the engineers.

Divide the total salary of the engineers by the number of engineers (25):

$\text{Average Salary of an Engineer}=\frac{1350000}{25}=54000\text{rupees}$

Thus, the average salary of the engineers is 54000 rupees.