The average salary of all workers in a workshop is Rs.12000. The average salary of 7 technicians is Rs .15000 and the average salary of the rest is Rs.9000. The total number of workers in the workshop is:

Options

A. 12
B. 13
C. 14
D. 15

Answer

To solve the problem step by step, let's define the variables and use the information given in the question.

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

### Step 2: Identify Technicians and Non-Technicians
We know that there are 7 technicians. Therefore, the number of non-technicians will be:
\[ X - 7 \]

### Step 3: Calculate Total Salaries
The average salary of all workers is Rs. 12000. Therefore, the total salary of all workers can be expressed as:
\[ \text{Total Salary} = 12000 \times X \]

The average salary of the 7 technicians is Rs. 15000, so their total salary is:
\[ \text{Total Salary of Technicians} = 7 \times 15000 = 105000 \]

The average salary of the non-technicians is Rs. 9000, so their total salary is:
\[ \text{Total Salary of Non-Technicians} = (X - 7) \times 9000 \]

### Step 4: Set Up the Equation
Now, we can set up the equation for the total salary:
\[ 12000X = 105000 + 9000(X - 7) \]

### Step 5: Expand and Simplify the Equation
Expanding the right side:
\[ 12000X = 105000 + 9000X - 63000 \]
Combining like terms:
\[ 12000X = 9000X + 42000 \]

### Step 6: Isolate \( X \)
Now, we will isolate \( X \) by subtracting \( 9000X \) from both sides:
\[ 12000X - 9000X = 42000 \]
\[ 3000X = 42000 \]

### Step 7: Solve for \( X \)
Dividing both sides by 3000:
\[ X = \frac{42000}{3000} = 14 \]

### Conclusion
The total number of workers in the workshop is:
\[ \boxed{14} \]