The average monthly salary of 30 employees and 5 managers is Rs. 800000. One manager with salar Rs. 180000 is replaced by a new manager. If the average monthly salary now becomes Rs. 78500, then what is the monthly salary of the new manager?

Options

A. Rs. 142500
B. Rs. 132000
C. Rs. 127500
D. Rs. 154500

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the total initial salary of the employees and managers.
The average monthly salary of 30 employees and 5 managers is given as Rs. 80,000. Therefore, the total number of individuals is:

\[ 30 + 5 = 35 \]

The total salary can be calculated as:

\[ \text{Total Salary} = \text{Average Salary} \times \text{Total Individuals} = 80,000 \times 35 = 2,800,000 \]

### Step 2: Calculate the total salary after replacing one manager.
One manager with a salary of Rs. 180,000 is replaced by a new manager. The total salary after replacing the manager will be:

\[ \text{New Total Salary} = \text{Old Total Salary} - \text{Old Manager's Salary} + \text{New Manager's Salary} \]

Let the salary of the new manager be \( X \). Thus,

\[ \text{New Total Salary} = 2,800,000 - 180,000 + X \]

### Step 3: Calculate the new average salary.
After the replacement, the average monthly salary becomes Rs. 78,500. Therefore, the new total salary can also be expressed as:

\[ \text{New Total Salary} = \text{New Average Salary} \times \text{Total Individuals} = 78,500 \times 35 = 2,747,500 \]

### Step 4: Set up the equation.
Now we have two expressions for the new total salary:

1. \( 2,800,000 - 180,000 + X \)
2. \( 2,747,500 \)

Setting these equal gives:

\[ 2,800,000 - 180,000 + X = 2,747,500 \]

### Step 5: Simplify and solve for \( X \).
Now, simplify the equation:

\[ 2,620,000 + X = 2,747,500 \]

Subtract \( 2,620,000 \) from both sides:

\[ X = 2,747,500 - 2,620,000 \]

Calculating the right side:

\[ X = 127,500 \]

### Conclusion
The monthly salary of the new manager is Rs. 127,500.

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