The average salary of the entire staff in an office is 3200 per month. The average salary of the Officers is 6800 and that of the Non-officers is 2000. If the number of Officers is 5, then find the number of Non-officers in the office.

Options

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

Answer

To solve the problem step by step, we will use the concept of averages and the allegation method.

### Step-by-Step Solution:

1. **Identify Given Information**:
- Average salary of the entire staff = Rs. 3200
- Average salary of Officers = Rs. 6800
- Average salary of Non-officers = Rs. 2000
- Number of Officers = 5

2. **Set Up the Allegation**:
- We will use the allegation method to find the ratio of Officers to Non-officers.
- The formula for allegation is:
\[ \text{Difference between Officer's average and overall average} = \text{Difference between overall average and Non-officer's average} \]

3. **Calculate Differences**:
- Difference between Officer's average and overall average:
\[ 6800 - 3200 = 3600 \]
- Difference between overall average and Non-officer's average:
\[ 3200 - 2000 = 1200 \]

4. **Set Up the Ratio**:
- The ratio of the number of Officers to Non-officers can be set up as:
\[ \frac{\text{Number of Officers}}{\text{Number of Non-officers}} = \frac{3600}{1200} \]
- Simplifying this gives:
\[ \frac{3600 \div 1200}{1200 \div 1200} = \frac{3}{1} \]
- This means for every 3 Non-officers, there is 1 Officer.

5. **Calculate the Number of Non-officers**:
- Let the number of Non-officers be \( x \).
- From the ratio we derived:
\[ \frac{5}{x} = \frac{1}{3} \]
- Cross-multiplying gives:
\[ 5 \cdot 3 = 1 \cdot x \implies x = 15 \]

6. **Conclusion**:
- The number of Non-officers in the office is **15**.