The average salary of the entire staff in a office is Rs 120 per month. The average salary of officers is Rs 460 and that of non-officers is Rs 110. If the number of officers is 15, then find the number of non-officers in the office.

Answer

To solve the problem step by step, we need to find the number of non-officers in the office given the average salaries and the number of officers.

### Step 1: Understand the Given Information
- Average salary of the entire staff = Rs 120
- Average salary of officers = Rs 460
- Average salary of non-officers = Rs 110
- Number of officers = 15

### Step 2: Set Up the Allegation
We can use the method of allegation to find the ratio of the number of officers to the number of non-officers.

1. Calculate the difference between the average salary of officers and the average salary of the entire staff:
\[ \text{Difference for officers} = 460 - 120 = 340 \]

2. Calculate the difference between the average salary of non-officers and the average salary of the entire staff:
\[ \text{Difference for non-officers} = 120 - 110 = 10 \]

### Step 3: Form the Ratio
Now, we can set up the ratio of the number of officers to the number of non-officers using the differences calculated:

\[ \text{Ratio} = \frac{\text{Difference for non-officers}}{\text{Difference for officers}} = \frac{10}{340} = \frac{1}{34} \]

This means for every 1 officer, there are 34 non-officers.

### Step 4: Calculate the Number of Non-Officers
We know that the number of officers is 15. Since the ratio of officers to non-officers is 1:34, we can find the number of non-officers as follows:

Let the number of non-officers be \( x \):
\[ \frac{1}{34} = \frac{15}{x} \]

Cross-multiplying gives:
\[ 1 \cdot x = 15 \cdot 34 \]
\[ x = 510 \]

### Conclusion
The number of non-officers in the office is **510**.

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