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, we will use the information provided about the average salaries of the workers, technicians, and the rest of the workers.

### Step 1: Understand the given information
- The average salary of all workers in the workshop = Rs. 12000
- The average salary of 7 technicians = Rs. 15000
- The average salary of the rest of the workers = Rs. 9000

### Step 2: Calculate the total salary of the technicians
To find the total salary of the technicians, we multiply the number of technicians by their average salary.
\[ \text{Total salary of technicians} = \text{Number of technicians} \times \text{Average salary of technicians} \]
\[ = 7 \times 15000 = 105000 \]

### Step 3: Let the number of other workers be \( x \)
We need to find the total number of workers in the workshop. Let \( x \) be the number of workers other than the technicians.

### Step 4: Calculate the total salary of the rest of the workers
The total salary of the rest of the workers can be calculated as:
\[ \text{Total salary of the rest} = x \times \text{Average salary of the rest} \]
\[ = x \times 9000 \]

### Step 5: Calculate the total salary of all workers
The total salary of all workers can be expressed as the sum of the total salary of technicians and the total salary of the rest:
\[ \text{Total salary of all workers} = \text{Total salary of technicians} + \text{Total salary of the rest} \]
\[ = 105000 + 9000x \]

### Step 6: Set up the equation using the average salary of all workers
The average salary of all workers is given by:
\[ \text{Average salary} = \frac{\text{Total salary of all workers}}{\text{Total number of workers}} \]
The total number of workers is \( 7 + x \). Therefore, we can set up the equation:
\[ 12000 = \frac{105000 + 9000x}{7 + x} \]

### Step 7: Cross-multiply to solve for \( x \)
Cross-multiplying gives:
\[ 12000(7 + x) = 105000 + 9000x \]
Expanding this:
\[ 84000 + 12000x = 105000 + 9000x \]

### Step 8: Rearranging the equation
Rearranging the equation to isolate \( x \):
\[ 12000x - 9000x = 105000 - 84000 \]
\[ 3000x = 21000 \]
\[ x = \frac{21000}{3000} = 7 \]

### Step 9: Calculate the total number of workers
The total number of workers in the workshop is:
\[ \text{Total workers} = 7 \text{ (technicians)} + x \text{ (rest)} = 7 + 7 = 14 \]

### Final Answer
The total number of workers in the workshop is **14**.

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