An organisation has 400 employees (officers and workers). The overall average monthly salary is Rs. 3000; officers average Rs. 10,000 and workers Rs. 2000. Find the numbers of officers and workers.

Introduction / Context:
This is a weighted average and mixture problem: the overall average salary is formed from two groups with known averages. Using total salary, we can determine how many belong to each category (officers vs. workers).

Given Data / Assumptions:

• Total employees = 400.
• Overall average = Rs. 3000 per month.
• Officer average = Rs. 10,000; worker average = Rs. 2000.

Concept / Approach:
Total salary = overall average * total employees. Let O be officers and W be workers with O + W = 400. Then 10000*O + 2000*W = total salary. Solve for O, then W = 400 − O.

Step-by-Step Solution:
Total salary = 3000 * 400 = Rs. 1,200,000. Equation: 10000O + 2000W = 1,200,000; also O + W = 400. Substitute W = 400 − O: 10000O + 2000(400 − O) = 1,200,000. 10000O + 800,000 − 2000O = 1,200,000 ⇒ 8000O = 400,000 ⇒ O = 50; W = 350.

Verification / Alternative check:
Check total salary: 50*10000 + 350*2000 = 500,000 + 700,000 = 1,200,000, which matches the overall figure.

Why Other Options Are Wrong:
300,100 or 250,150 or 310,90 do not satisfy both the headcount and salary equations simultaneously.

Common Pitfalls:
Misapplying averages (e.g., averaging 10,000 and 2,000 directly) or forgetting to multiply by counts to get total salary.

Final Answer:
50 , 350