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

Introduction / Context:
This question is another example of a weighted average problem with two subgroups: technicians and other workers. You are given the average salary of each subgroup and the overall average salary. Your job is to determine how many workers there are in total. This type of question is very common in quantitative aptitude tests involving mixtures, groups, and weighted averages.

Given Data / Assumptions:

• The average salary of all workers is Rs 8000 per month.
• There are 7 technicians.
• The average salary of the 7 technicians is Rs 12000 per month.
• The average salary of the remaining workers is Rs 6000 per month.
• We must find the total number of workers in the workshop.

Concept / Approach:
We again use the weighted average idea. If the total number of workers is N, then the overall total salary is 8000 * N. The total salary can also be expressed as the sum of the total salary of technicians plus the total salary of the remaining workers. Equating these two forms allows us to solve for N.

Step-by-Step Solution:
Let the total number of workers be N.Overall average salary is Rs 8000, so total salary = 8000 * N.There are 7 technicians with an average salary of Rs 12000.Total salary of technicians = 7 * 12000 = Rs 84000.The remaining workers are (N - 7) in number, with average salary Rs 6000.Total salary of remaining workers = (N - 7) * 6000.Total salary of all workers can also be written as 84000 + 6000 * (N - 7).Equate both expressions: 8000N = 84000 + 6000(N - 7).Expand: 8000N = 84000 + 6000N - 42000.Simplify: 8000N = 6000N + 42000, so 2000N = 42000.Therefore, N = 42000 / 2000 = 21 workers.

Verification / Alternative check:
If there are 21 workers, 7 are technicians and 14 are other workers. Salary of technicians = 7 * 12000 = Rs 84000. Salary of remaining 14 workers = 14 * 6000 = Rs 84000. Total salary = 84000 + 84000 = Rs 168000. Average salary = 168000 / 21 = Rs 8000, which matches the given overall average.

Why Other Options Are Wrong:
If N were 20 or 24, the overall average would not be Rs 8000. Too few workers or too many workers would skew the weighted average. For example, with fewer low-salary workers, the average would be closer to Rs 12000, and with more, closer to Rs 6000. Only 21 produces the correct balance to maintain an overall average of Rs 8000.

Common Pitfalls:
Some learners mistakenly average 12000 and 6000 to get 9000, not noticing that the group sizes are different. Others forget to subtract 7 when determining how many workers are not technicians. Always use total salary expressions and equate them according to the weighted average formula.

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