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

Introduction / Context:
This question involves the concept of average salary and how it changes when an additional salary is added to the group. It is a common type of aptitude problem that tests your understanding of how total sums and averages are related and how to work backwards to find an individual value from a change in the average.

Given Data / Assumptions:

• Number of employees initially (excluding the manager) = 24.
• Average salary of these 24 employees = Rs. 1500 per month.
• When the manager is included, there are 25 people in total.
• The new average salary including the manager increases by Rs. 400, so the new average is Rs. 1900 per month.
• We must find the manager's monthly salary.

Concept / Approach:
Average salary is total salary divided by the number of people. We can first compute the total salary of the 24 employees using their average. Then we compute the new total salary when the manager is included using the new average for 25 people. The difference between these two totals gives the manager's salary. This is a simple but powerful approach that can be used for many average related problems.

Step-by-Step Solution:
Step 1: Compute the total salary of the 24 employees. Total salary (24 employees) = 24 * 1500 = 36,000. Step 2: When the manager is included, total number of people = 25. Step 3: New average salary = 1500 + 400 = 1900. Step 4: Total salary (24 employees plus manager) = 25 * 1900 = 47,500. Step 5: Manager's salary = Total salary (25) - Total salary (24) = 47,500 - 36,000. Step 6: Compute the difference: 47,500 - 36,000 = 11,500. Step 7: Therefore, the manager's monthly salary is Rs. 11,500.

Verification / Alternative check:
Verify by recomputing the average. Add the manager's salary to the total for 24 employees: 36,000 + 11,500 = 47,500. Divide this by 25 people to find the new average: 47,500 / 25 = 1900. Since this matches the stated new average of Rs. 1900, our calculation for the manager's salary is confirmed as correct.

Why Other Options Are Wrong:
If the manager's salary were Rs. 8840, the new total would be 44,840, giving an average of 44,840 / 25, which is less than 1900. Salaries such as Rs. 12,800 or Rs. 9450 or Rs. 15,000 also fail to produce the required new average of Rs. 1900 when added to the original total. Only Rs. 11,500 leads to the correct increase in average by exactly Rs. 400.

Common Pitfalls:
Sometimes students mistakenly divide the increase in total salary by the wrong number of people or miscalculate the new average. Others might incorrectly think the manager's salary is simply 1900 plus some difference instead of using total sums. Always remember that changes in average reflect changes in total, and the difference between new and old totals gives the contribution of the added person.

Final Answer:
The manager's monthly salary is Rs. 11,500.