The average salary per head of all the workers in a workshop is ₹850 if the average salary per head of 7 techniques is ₹1000 and the average salary per head of the rest is ₹780 the total number of workers in the workshop is

Options

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

Answer

To solve the problem step by step, we will use the concept of averages and the allegation method.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Average salary of all workers = ₹850
- Average salary of 7 technicians = ₹1000
- Average salary of the rest of the workers = ₹780

2. **Set Up the Allegation Method**:
- We will use the allegation method to find the ratio of the number of technicians to the number of other workers.
- Write the average salaries in a way that allows us to compare them:
```
Technicians: ₹1000
All Workers: ₹850
Others: ₹780
```

3. **Calculate the Differences**:
- Find the difference between the average salary of the technicians and the overall average:
\[ 1000 - 850 = 150 \]
- Find the difference between the overall average and the average salary of the other workers:
\[ 850 - 780 = 70 \]

4. **Set Up the Ratio**:
- The ratio of the number of technicians to the number of other workers is given by the differences calculated:
\[ \text{Ratio} = \frac{\text{Difference for Others}}{\text{Difference for Technicians}} = \frac{70}{150} \]
- Simplifying this ratio:
\[ \frac{70}{150} = \frac{7}{15} \]

5. **Calculate Total Workers**:
- Let the number of technicians be \(7\) (as given).
- Let the number of other workers be \(x\).
- According to the ratio, if technicians are \(7\), then the number of other workers is \(15\) (since the ratio is \(7:15\)).
- Therefore, the total number of workers is:
\[ 7 + 15 = 22 \]

### Final Answer:
The total number of workers in the workshop is **22**.