The average salary of the school staff in a school is Rs 4800 per month. The average salary of teachers is Rs 8000 and that of non-teachers is Rs 4000 . If the number of teachers are 6 , then find number of non-teachers in the school ?

Options

A. 8
B. 12
C. 15
D. 5

Explanation

To solve the problem step by step, we will use the concept of averages and the relationship between the number of teachers and non-teachers.

### Step 1: Understand the given data
- Average salary of the school staff = Rs 4800
- Average salary of teachers = Rs 8000
- Average salary of non-teachers = Rs 4000
- Number of teachers = 6

### Step 2: Set up the equation using the average formula
The average salary of the entire staff can be calculated using the formula:

\[ \text{Average} = \frac{\text{Total Salary}}{\text{Total Number of Staff}} \]

Let the number of non-teachers be \( n \). Therefore, the total number of staff is \( 6 + n \).

### Step 3: Calculate total salaries
The total salary of teachers can be calculated as:
\[ \text{Total Salary of Teachers} = \text{Number of Teachers} \times \text{Average Salary of Teachers} = 6 \times 8000 = 48000 \]

The total salary of non-teachers can be calculated as:
\[ \text{Total Salary of Non-Teachers} = n \times 4000 \]

### Step 4: Write the equation for total salary
Now, we can write the equation for the total salary of all staff:
\[ \text{Total Salary} = \text{Total Salary of Teachers} + \text{Total Salary of Non-Teachers} \]
\[ \text{Total Salary} = 48000 + 4000n \]

### Step 5: Set up the average equation
Now, substituting this into the average formula:
\[ 4800 = \frac{48000 + 4000n}{6 + n} \]

### Step 6: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ 4800(6 + n) = 48000 + 4000n \]

### Step 7: Expand and simplify
Expanding the left side:
\[ 28800 + 4800n = 48000 + 4000n \]

Now, rearranging the equation:
\[ 4800n - 4000n = 48000 - 28800 \]
\[ 800n = 19200 \]

### Step 8: Solve for \( n \)
Dividing both sides by 800:
\[ n = \frac{19200}{800} = 24 \]

### Conclusion
The number of non-teachers in the school is **24**.

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