The average monthly salary of the workers in a workshop is Rs. 8500. if the average monthly salary of 7 technicians is Rs. 10,000 and the average monthly salary of the rest is Rs. 7800, the total number of workers in the workshop is

Options

A. 18
B. 20
C. 22
D. 24

Answer

To solve the problem, we need to find the total number of workers in the workshop based on the average salaries provided.

### Step-by-Step Solution:

1. **Define Variables**:
Let the total number of workers in the workshop be \( N \).

2. **Calculate Total Salary of All Workers**:
The average monthly salary of all workers is Rs. 8500. Therefore, the total salary of all workers can be calculated as:
\[ \text{Total Salary of All Workers} = N \times 8500 \]

3. **Calculate Total Salary of Technicians**:
The average monthly salary of the 7 technicians is Rs. 10,000. Thus, the total salary of the technicians is:
\[ \text{Total Salary of Technicians} = 7 \times 10000 = 70000 \]

4. **Calculate Number of Remaining Workers**:
The remaining workers are \( N - 7 \). The average monthly salary of these remaining workers is Rs. 7800. Therefore, the total salary of the remaining workers is:
\[ \text{Total Salary of Remaining Workers} = (N - 7) \times 7800 \]

5. **Set Up the Equation**:
The total salary of all workers is the sum of the total salary of the technicians and the total salary of the remaining workers:
\[ N \times 8500 = 70000 + (N - 7) \times 7800 \]

6. **Expand and Simplify the Equation**:
Expanding the right side:
\[ N \times 8500 = 70000 + 7800N - 54600 \]
Simplifying gives:
\[ N \times 8500 = 23400 + 7800N \]

7. **Rearranging the Equation**:
Move all terms involving \( N \) to one side:
\[ 8500N - 7800N = 23400 \]
This simplifies to:
\[ 700N = 23400 \]

8. **Solve for \( N \)**:
Divide both sides by 700:
\[ N = \frac{23400}{700} = 33.42857 \]
Since the number of workers must be a whole number, we round it to the nearest whole number, which is 34.

### Conclusion:
The total number of workers in the workshop is **34**.