The average monthly salary of all the employees in a firm is Rs 60. Among them, 12 officers receive an average salary of Rs 400 per month and the remaining employees receive an average salary of Rs 56 per month. Find the total number of employees working in the firm.

Introduction / Context:
This is a classic weighted average salary problem where a group is divided into two subgroups with different averages. The overall average is known, and the average of each subgroup is known. The question asks for the total number of employees, which requires setting up an equation based on total salary paid to all employees.

Given Data / Assumptions:

• The average salary of all employees is Rs 60 per month.
• There are 12 officers.
• The average salary of the 12 officers is Rs 400 per month.
• The remaining employees (non-officers) have an average salary of Rs 56 per month.
• We must find the total number of employees in the firm.

Concept / Approach:
We use the idea of weighted averages: overall average = (total salary of all employees) / (total number of employees). If the total number of employees is N, then the total salary can be expressed in terms of N and the given subgroup averages. By equating this to the expression derived from the overall average, we get a linear equation in N that we can solve.

Step-by-Step Solution:
Let the total number of employees be N.Overall average salary = Rs 60, so total salary of all employees = 60 * N.We know there are 12 officers with an average salary of Rs 400.Total salary of officers = 12 * 400 = Rs 4800.The remaining employees are (N - 12) in number, each earning on average Rs 56.Total salary of remaining employees = (N - 12) * 56.Total salary of all employees can also be written as 4800 + 56 * (N - 12).Equate both expressions for total salary: 60N = 4800 + 56(N - 12).Expand the right side: 60N = 4800 + 56N - 672.So 60N = 56N + 4128, hence 4N = 4128.Therefore, N = 4128 / 4 = 1032 employees.

Verification / Alternative check:
If there are 1032 employees, 12 are officers and 1020 are non-officers. Salary of officers = 12 * 400 = Rs 4800. Salary of non-officers = 1020 * 56 = Rs 57120. Total salary = 4800 + 57120 = Rs 61920. Average salary = 61920 / 1032 = Rs 60, exactly as given. Hence, the calculation is correct.

Why Other Options Are Wrong:
If you try 1030, 1060 or any other option, the recomputed overall average will differ from Rs 60. For example, a smaller N would make the overall average higher than 60 because the officers get a much larger salary. A larger N would pull the overall average closer to Rs 56. Only N = 1032 satisfies the weighted average condition.

Common Pitfalls:
Common mistakes include failing to subtract 12 when calculating the number of non-officers, or trying to average 400 and 56 directly without using proper weights. Always express total salary in two ways (overall and by groups) and then equate them to derive a correct equation.

Final Answer:
The total number of employees in the firm is 1032.