The average salary of the entire staff in an office is Rs 200 per day. The average salary of officers is Rs 550 and that of non-officers is Rs 120. If the number of officers is 16, then find the numbers of non-officers in the office.

Answer

To solve the problem step by step, we will use the concept of weighted averages.

### Step 1: Identify the given information
- Average salary of the entire staff (A) = Rs 200
- Average salary of officers (A1) = Rs 550
- Average salary of non-officers (A2) = Rs 120
- Number of officers (n1) = 16
- Number of non-officers (n2) = ?

### Step 2: Use the formula for weighted average
The formula for the average salary of the entire staff can be expressed as:
\[ A = \frac{A1 \cdot n1 + A2 \cdot n2}{n1 + n2} \]
Substituting the known values into the formula:
\[ 200 = \frac{550 \cdot 16 + 120 \cdot n2}{16 + n2} \]

### Step 3: Calculate the total salary of officers
Calculate \(550 \cdot 16\):
\[ 550 \cdot 16 = 8800 \]

### Step 4: Substitute the total salary of officers into the equation
Now, substitute this value back into the equation:
\[ 200 = \frac{8800 + 120 \cdot n2}{16 + n2} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ 200 \cdot (16 + n2) = 8800 + 120 \cdot n2 \]

### Step 6: Distribute the 200 on the left side
Distributing gives:
\[ 3200 + 200 \cdot n2 = 8800 + 120 \cdot n2 \]

### Step 7: Rearrange the equation
Now, rearranging the equation to isolate \(n2\):
\[ 200 \cdot n2 - 120 \cdot n2 = 8800 - 3200 \]
\[ 80 \cdot n2 = 5600 \]

### Step 8: Solve for \(n2\)
Now, divide both sides by 80:
\[ n2 = \frac{5600}{80} = 70 \]

### Conclusion
The number of non-officers in the office is **70**.

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