Two-group salary mix: The average salary across all workers is Rs 850. Seven technicians average Rs 1000 each. The rest average Rs 780 each. How many total workers are there in the workshop?

Introduction / Context:
Another two-group mixture. With the overall average and one subgroup known, solve for total headcount by equating totals and using the other subgroup’s average.

Given Data / Assumptions:

• Overall average = Rs 850.
• Technicians: 7 people, average = Rs 1000.
• Others: average = Rs 780, count unknown.

Concept / Approach:
Let total workers be n. Then total payroll = 850*n. Also equals 7*1000 + (n - 7)*780. Solve for n.

Step-by-Step Solution:

Verification / Alternative check:
Totals: technicians = 7000; others = 15*780 = 11700; grand = 18700; 18700/22 = 850.\n

Why Other Options Are Wrong:

• 18, 20, 24: Do not satisfy the weighted-average equality.

Common Pitfalls:
Misplacing parentheses in (n - 7)*780 or equating averages instead of totals.

Final Answer: