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 option is 54000.

Let us break down the problem step-by-step to understand how to arrive at this answer.

Step 1: Understand the initial state of the employees' salaries
The company has 5 managers and 25 engineers, making a total of 30 employees.
The initial average salary of these 30 employees is 60,000 rupees.
Therefore, the total initial salary of all 30 employees can be calculated as:
$$\text{Total Initial Salary}=30\times \mathrm{60,000}=\mathrm{1,800,000}\text{rupees}$$
Let the average salary of the managers be $S_m$ and the average salary of the engineers be $S_e$.
The sum of the salaries of the 5 managers is $5S_m$, and the sum of the salaries of the 25 engineers is $25S_e$.
So, we can write our first equation:
$$5S_m+25S_e=\mathrm{1,800,000}$$
Dividing the entire equation by 5 simplifies it to:
$$S_m+5S_e=\mathrm{360,000}$$
We will refer to this as Equation (1).

Step 2: Analyze the effect of the salary increase
Each of the 5 managers receives a 20% salary increase, while the engineers' salaries remain unchanged.
A 20% increase in each manager's salary means the total increase in the managers' salary pool is:
$$\text{Increase in Managers' Total Salary}=0.20\times (5S_m)=S_m$$
This increase in the total salary pool causes the average salary of all 30 employees to increase by 5%.
The increase in the overall average salary is:
$$5\%\text{of}\mathrm{60,000}=0.05\times \mathrm{60,000}=\mathrm{3,000}\text{rupees}$$
The total increase in the salary pool of all 30 employees is:
$$\text{Total Increase in Salaries}=30\times \mathrm{3,000}=\mathrm{90,000}\text{rupees}$$
Since the only source of this increase is the managers' 20% raise, the total increase in managers' salary must equal this total salary pool increase:
$$S_m=\mathrm{90,000}\text{rupees}$$
Thus, the average salary of the managers ($S_m$) is 90,000 rupees.

Step 3: Solve for the average salary of the engineers
Now we substitute the value of $S_m$ into Equation (1):
$$\mathrm{90,000}+5S_e=\mathrm{360,000}$$
Subtract 90,000 from both sides:
$$5S_e=\mathrm{270,000}$$
Divide by 5 to find $S_e$:
$$S_e=\frac{\mathrm{270,000}}{5}=\mathrm{54,000}$$
Therefore, the average salary of the engineers is 54,000 rupees.