The average monthly salary of 24 employees in an organisation is Rs 1500. When the manager salary is included the average monthly salary increases by Rs 400. What is the monthly salary of the manager?

Introduction:
This question tests your understanding of how adding one more data point affects the average of a group. The average salary of employees is known, and we are told how the average changes after including the manager. Using these values, we can find the manager salary.

Given Data / Assumptions:
- Number of employees initially considered = 24. - Average salary of these 24 employees = Rs 1500 per month. - After including the manager, number of people considered = 25. - New average salary after including the manager is Rs 1500 + Rs 400 = Rs 1900 per month. - We must find the manager monthly salary.

Concept / Approach:
Average salary is total salary divided by number of people. First, we compute the total salary of the 24 employees using the initial average. Then we compute the new total salary of 25 people using the new average. The difference between the new total and the old total is the salary of the manager.

Step-by-Step Solution:
Step 1: Total salary of 24 employees = 24 * 1500. Step 2: 24 * 1500 = 36000, so the sum of salaries of the 24 employees is Rs 36000. Step 3: After including the manager, there are 25 people with an average salary of Rs 1900. Step 4: Total salary of 25 people = 25 * 1900. Step 5: 25 * 1900 = 47500, so the new total salary is Rs 47500. Step 6: The manager salary is the difference between the new total and the old total. Step 7: Manager salary = 47500 - 36000 = 11500.

Verification / Alternative Check:
Check the average after including the manager. If the manager salary is Rs 11500, the total salary of 25 people is 36000 + 11500 = 47500. Dividing by 25 gives 47500 / 25 = 1900, which matches the new average stated in the problem. This confirms that the manager salary is correctly calculated.

Why Other Options Are Wrong:
Options Rs 8840, Rs 12800, Rs 9450 and Rs 15000 do not produce the required new average of Rs 1900 when added to Rs 36000 and divided by 25. They either give a higher or lower average than specified.

Common Pitfalls:
Some candidates may forget to add the increase in average to the original average, or they might incorrectly multiply the new average by 24 instead of 25. Another mistake is to average the original average and the new average instead of working with totals. Always remember that total = average * number of items is the key relation.

Final Answer:
The monthly salary of the manager is Rs 11500.