The average salary, per head, of all the workers of an institution is Indian rupee/Symbol ₹ 60. The average salary of 12 officers isIndian rupee/Symbol ₹ 400, the average salary, per head of the rest isIndian rupee/Symbol ₹ 56. The total number of workers in the institution is

Options

A. 1030
B. 1035
C. 1020
D. 1032

Answer

To find the total number of workers in the institution, we will use the information provided about the average salaries of different groups of workers. Let's break it down step by step.

### Step-by-Step Solution:

1. **Define Variables**:
- Let \( x \) be the total number of workers in the institution.
- The average salary of all workers is ₹60.
- The average salary of 12 officers is ₹400.
- The average salary of the remaining workers is ₹56.

2. **Calculate Total Salary of All Workers**:
- The total salary of all workers can be calculated as:
\[ \text{Total Salary} = \text{Average Salary} \times \text{Total Workers} = 60x \]

3. **Calculate Total Salary of Officers**:
- The total salary of the 12 officers is:
\[ \text{Total Salary of Officers} = 12 \times 400 = 4800 \]

4. **Calculate Total Salary of Remaining Workers**:
- The number of remaining workers is \( x - 12 \).
- The total salary of the remaining workers can be calculated as:
\[ \text{Total Salary of Remaining Workers} = (x - 12) \times 56 \]

5. **Set Up the Equation**:
- The total salary of all workers is the sum of the total salary of the officers and the total salary of the remaining workers:
\[ 60x = 4800 + (x - 12) \times 56 \]

6. **Expand and Simplify the Equation**:
- Expanding the right side:
\[ 60x = 4800 + 56x - 672 \]
- Combine like terms:
\[ 60x = 56x + 4128 \]

7. **Isolate \( x \)**:
- Subtract \( 56x \) from both sides:
\[ 60x - 56x = 4128 \]
\[ 4x = 4128 \]
- Divide both sides by 4:
\[ x = \frac{4128}{4} = 1032 \]

8. **Conclusion**:
- The total number of workers in the institution is \( 1032 \).