The average monthly salary of employees, consisting of officers and workers, of an organisation is 3000. The average salary of an officer is 10,000 while that of a worker is 2000 per month. If there are total 400 employees in the organisation, find the number of officers.

Options

A. 60
B. 50
C. 80
D. 40

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the given information
We know:
- Average salary of all employees = 3000
- Average salary of an officer = 10,000
- Average salary of a worker = 2000
- Total number of employees = 400

### Step 2: Set up the ratios using the allegation method
Using the allegation method, we can find the ratio of officers to workers based on their salaries.

1. The difference between the average salary of an officer and the overall average:
\[ 10,000 - 3,000 = 7,000 \]

2. The difference between the overall average and the average salary of a worker:
\[ 3,000 - 2,000 = 1,000 \]

### Step 3: Establish the ratio of officers to workers
From the differences calculated:
- The ratio of officers to workers can be expressed as:
\[ \text{Officers : Workers} = 1,000 : 7,000 \]
Simplifying this gives:
\[ \text{Officers : Workers} = 1 : 7 \]

### Step 4: Define the number of officers and workers
Let the number of officers be \( x \). Then, the number of workers will be \( 7x \).

### Step 5: Set up the equation based on total employees
According to the problem, the total number of employees is 400:
\[ x + 7x = 400 \]
This simplifies to:
\[ 8x = 400 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 8:
\[ x = \frac{400}{8} = 50 \]

### Step 7: Conclusion
Thus, the number of officers in the organization is \( 50 \).

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