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

Options

A. (a) 20
B. (b) 22
C. (c) 25
D. (d) 28

Answer

To find the total number of workers in the workshop, we can follow these steps:

### Step 1: Define the Variables
Let the total number of workers in the workshop be \( x \).

### Step 2: Calculate the Total Salary of Technicians
The average salary of 7 technicians is given as Rs. 10,000. Therefore, the total salary of the technicians can be calculated as:
\[ \text{Total Salary of Technicians} = 7 \times 10,000 = 70,000 \]

### Step 3: Calculate the Total Salary of Remaining Workers
The average salary of the remaining workers (which is \( x - 7 \)) is Rs. 7,800. Therefore, the total salary of the remaining workers can be calculated as:
\[ \text{Total Salary of Remaining Workers} = (x - 7) \times 7,800 \]

### Step 4: Set Up the Equation for the Average Salary
The average salary of all workers is Rs. 8,500. The total salary of all workers can be expressed as the sum of the salaries of technicians and remaining workers:
\[ \text{Total Salary of All Workers} = 70,000 + (x - 7) \times 7,800 \]
The average salary can be expressed as:
\[ \text{Average Salary} = \frac{\text{Total Salary of All Workers}}{x} \]
Substituting the values we have:
\[ 8500 = \frac{70,000 + (x - 7) \times 7,800}{x} \]

### Step 5: Multiply Both Sides by \( x \) to Eliminate the Denominator
\[ 8500x = 70,000 + (x - 7) \times 7,800 \]

### Step 6: Expand the Equation
Expanding the right side gives:
\[ 8500x = 70,000 + 7,800x - 54,600 \]
Simplifying this:
\[ 8500x = 70,000 - 54,600 + 7,800x \]
\[ 8500x = 15,400 + 7,800x \]

### Step 7: Rearranging the Equation
Subtract \( 7,800x \) from both sides:
\[ 8500x - 7800x = 15,400 \]
\[ 700x = 15,400 \]

### Step 8: Solve for \( x \)
Dividing both sides by 700:
\[ x = \frac{15,400}{700} = 22 \]

### Conclusion
The total number of workers in the workshop is \( \boxed{22} \).

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