The mean monthly salary of 8 teachers is ₹ 32,000. When the salary of one senior teacher is included their mean becomes ₹ 33,500. Find the salary of the senior teacher.

Options

A. 42500
B. 45000
C. 42000
D. 45500

Answer

To find the salary of the senior teacher, we can follow these steps:

### Step 1: Calculate the total salary of the 8 teachers.
The mean salary of the 8 teachers is given as ₹32,000. To find the total salary (S) of these teachers, we can use the formula:

\[ S = \text{Mean} \times \text{Number of Teachers} \]

Substituting the values:

\[ S = 32,000 \times 8 = 256,000 \]

### Step 2: Set up the equation for the new mean salary including the senior teacher.
When the salary of the senior teacher is included, the new mean salary becomes ₹33,500 for a total of 9 teachers. We can express this as:

\[ \text{New Mean} = \frac{S + X}{9} \]

Where \(X\) is the salary of the senior teacher.

### Step 3: Substitute the known values into the equation.
We know that the new mean is ₹33,500, so we can set up the equation:

\[ 33,500 = \frac{256,000 + X}{9} \]

### Step 4: Multiply both sides by 9 to eliminate the fraction.
\[ 33,500 \times 9 = 256,000 + X \]

Calculating the left side:

\[ 301,500 = 256,000 + X \]

### Step 5: Solve for \(X\).
To find the salary of the senior teacher, we need to isolate \(X\):

\[ X = 301,500 - 256,000 \]

Calculating the right side:

\[ X = 45,500 \]

### Conclusion:
The salary of the senior teacher is ₹45,500.

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