The average monthly salary of the workers in a work shop 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 work shop is

Options

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

Answer

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

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

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

### Step 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:
\[ \text{Total Salary of Technicians} = \text{Average Salary of Technicians} \times \text{Number of Technicians} = 10000 \times 7 = 70000 \]

### Step 4: Calculate Total Salary of Remaining Workers
Let the number of remaining workers be \( n - 7 \). The average monthly salary of the remaining workers is Rs. 7800. Therefore, the total salary of the remaining workers is:
\[ \text{Total Salary of Remaining Workers} = \text{Average Salary of Remaining Workers} \times \text{Number of Remaining Workers} = 7800 \times (n - 7) \]

### Step 5: Set Up the Equation
Now, we can set up the equation for the total salary:
\[ \text{Total Salary} = \text{Total Salary of Technicians} + \text{Total Salary of Remaining Workers} \]
Substituting the values we calculated:
\[ 8500n = 70000 + 7800(n - 7) \]

### Step 6: Simplify the Equation
Expanding the right side:
\[ 8500n = 70000 + 7800n - 54600 \]
Combining like terms:
\[ 8500n = 23400 + 7800n \]

### Step 7: Solve for \( n \)
Rearranging the equation:
\[ 8500n - 7800n = 23400 \]
\[ 700n = 23400 \]
Dividing both sides by 700:
\[ n = \frac{23400}{700} = 33.42857 \]
Since \( n \) must be a whole number, we round it to the nearest whole number:
\[ n = 34 \]

### Conclusion
Thus, the total number of workers in the workshop is \( n = 34 \).

---