The average salary of staff of company is Rs. 1200. If the average salary of officers is Rs. 4600 & that of non-officers is Rs. 1100. If the no. of officers are 15. Find the no. of non-officers.

Answer

To solve the problem step by step, we will use the method of alligation.

### Step 1: Identify the given data
- Average salary of the staff (overall) = Rs. 1200
- Average salary of officers = Rs. 4600
- Average salary of non-officers = Rs. 1100
- Number of officers = 15

### Step 2: Set up the alligation
We will set up the alligation by placing the average salaries in a way that allows us to find the ratio of officers to non-officers.

```
Officers: Rs. 4600
Overall: Rs. 1200
Non-Officers: Rs. 1100
```

### Step 3: Calculate the differences
Now, we calculate the differences between the average salaries:

- Difference between officers and overall salary:
\[ 4600 - 1200 = 3400 \]

- Difference between non-officers and overall salary:
\[ 1200 - 1100 = 100 \]

### Step 4: Set up the ratio
The ratio of the number of officers to the number of non-officers can be set up using the differences calculated:

\[ \text{Ratio of officers to non-officers} = \frac{3400}{100} = 34:1 \]

### Step 5: Calculate the number of non-officers
Let the number of non-officers be \( x \). According to the ratio, we have:

\[ \frac{15}{x} = \frac{34}{1} \]

Cross-multiplying gives us:

\[ 15 \cdot 1 = 34 \cdot x \]

This simplifies to:

\[ 15 = 34x \]

Now, solving for \( x \):

\[ x = \frac{15}{34} \]

### Step 6: Calculate the value of \( x \)
To find the number of non-officers, we need to express it in whole numbers. Since the ratio is 34:1, we can multiply both sides by a common factor to find the actual number of non-officers.

If we assume \( k \) is the common multiplier, we have:

\[ 15 = 34k \implies k = \frac{15}{34} \]

Now, substituting back to find \( x \):

\[ x = k = \frac{15}{34} \cdot 1 = \frac{15}{34} \cdot 34 = 15 \]

Thus, the number of non-officers is:

\[ x = 15 \]

### Final Answer
The number of non-officers is 15.

---