The average salary of all workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the remaining workers is Rs. 6000. What is the total number of workers in the workshop?

Introduction / Context:
This is another mixture and average problem involving salaries in a workshop. The overall average salary is known, along with the number and average salary of technicians and the average salary of the remaining workers. Your task is to find the total number of workers. Such questions are helpful in understanding how subgroups with different averages combine to form an overall average.

Given Data / Assumptions:
- Let the total number of workers be N.
- Average salary of all workers = Rs. 8000.
- Number of technicians = 7.
- Average salary of technicians = Rs. 12000.
- Average salary of the remaining workers = Rs. 6000.
- We have to find N.

Concept / Approach:
The overall total salary equals the sum of the salaries of technicians and the salaries of all the other workers. The overall average multiplied by N gives the total salary in one expression. Another expression for the total salary comes from adding the subgroup totals. Equating these two expressions allows us to compute N.

Step-by-Step Solution:
Step 1: Total salary of all workers = 8000 * N.Step 2: Total salary paid to 7 technicians = 7 * 12000 = Rs. 84000.Step 3: Number of remaining workers = N - 7.Step 4: Total salary paid to remaining workers = (N - 7) * 6000.Step 5: Total salary can also be written as 84000 + 6000 * (N - 7).Step 6: Equate the two expressions for total salary: 8000N = 84000 + 6000(N - 7).Step 7: Expand the right side: 8000N = 84000 + 6000N - 42000.Step 8: Simplify: 8000N = 6000N + 42000.Step 9: Subtract 6000N: 2000N = 42000.Step 10: N = 42000 / 2000 = 21.

Verification / Alternative Check:
If N = 21, then remaining workers = 21 - 7 = 14. Salary for technicians = 84000. Salary for remaining workers = 14 * 6000 = 84000. Total salary = 84000 + 84000 = 168000. Average salary = 168000 / 21 = 8000, which matches the given overall average. This confirms that N = 21 is correct.

Why Other Options Are Wrong:
If N were 20, 23 or 24, the total salary computed from subgroup averages would not equal 8000 times N. A quick substitution shows that the equation 8000N = 84000 + 6000(N - 7) is not satisfied for those values, so they cannot be the total number of workers.

Common Pitfalls:
Some students mistakenly apply a simple average formula like (12000 + 6000) / 2, ignoring the different group sizes. Others forget to subtract 7 when finding the number of non technicians. The correct technique is always to use totals: overall total salary equals the sum of subgroup totals.

Final Answer:
The total number of workers in the workshop is 21.