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.

Answer

To find the salary of the senior teacher, we will 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. We can calculate the total salary of these 8 teachers using the formula for mean:

\[ \text{Mean} = \frac{\text{Total Salary}}{\text{Number of Teachers}} \]

Thus, the total salary of the 8 teachers can be calculated as:

\[ \text{Total Salary of 8 teachers} = \text{Mean} \times \text{Number of Teachers} = 32,000 \times 8 \]

Calculating this gives:

\[ \text{Total Salary of 8 teachers} = 32,000 \times 8 = 256,000 \]

### Step 2: Calculate the total salary of the 9 teachers
When the salary of the senior teacher is included, the mean salary of the 9 teachers becomes ₹33,500. We can calculate the total salary of these 9 teachers using the same formula for mean:

\[ \text{Total Salary of 9 teachers} = \text{Mean} \times \text{Number of Teachers} = 33,500 \times 9 \]

Calculating this gives:

\[ \text{Total Salary of 9 teachers} = 33,500 \times 9 = 301,500 \]

### Step 3: Find the salary of the senior teacher
To find the salary of the senior teacher, we can subtract the total salary of the 8 teachers from the total salary of the 9 teachers:

\[ \text{Salary of Senior Teacher} = \text{Total Salary of 9 teachers} - \text{Total Salary of 8 teachers} \]

Substituting the values we calculated:

\[ \text{Salary of Senior Teacher} = 301,500 - 256,000 \]

Calculating this gives:

\[ \text{Salary of Senior Teacher} = 45,500 \]

### Final Answer
The salary of the senior teacher is **₹45,500**.

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