The average salary per head of all workers of an institution isर 60. The average salary per head of 12 officers is र 400. The average salary per head of the rest is र 56. Then, the total number of workers in the institution is

Options

A. 1030
B. 1032
C. 1062
D. 1060

Answer

To solve the problem step by step, we need to find the total number of workers in the institution based on the given average salaries.

### Step 1: Understand the given information
- Average salary of all workers = Rs. 60
- Average salary of 12 officers = Rs. 400
- Average salary of the rest of the workers = Rs. 56

### Step 2: Let the total number of workers be \( N \)
We know that the total number of workers consists of 12 officers and the remaining workers. Thus, the number of remaining workers = \( N - 12 \).

### Step 3: Calculate the total salary of all workers
The total salary of all workers can be expressed as:
\[ \text{Total Salary} = \text{Average Salary} \times \text{Total Number of Workers} = 60N \]

### Step 4: Calculate the total salary of the officers
The total salary of the 12 officers can be calculated as:
\[ \text{Total Salary of Officers} = \text{Average Salary of Officers} \times \text{Number of Officers} = 400 \times 12 = 4800 \]

### Step 5: Calculate the total salary of the remaining workers
The total salary of the remaining workers can be expressed as:
\[ \text{Total Salary of Remaining Workers} = \text{Average Salary of Remaining Workers} \times \text{Number of Remaining Workers} = 56(N - 12) \]

### Step 6: Set up the equation
Since the total salary of all workers is the sum of the total salary of the officers and the total salary of the remaining workers, we can set up the equation:
\[ 60N = 4800 + 56(N - 12) \]

### Step 7: Simplify the equation
Expanding the right side:
\[ 60N = 4800 + 56N - 672 \]
\[ 60N = 56N + 4128 \]

### Step 8: Solve for \( N \)
Subtract \( 56N \) from both sides:
\[ 60N - 56N = 4128 \]
\[ 4N = 4128 \]
Now, divide by 4:
\[ N = \frac{4128}{4} = 1032 \]

### Step 9: Conclusion
The total number of workers in the institution is \( N = 1032 \).

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