The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager’s salary is added, the average salary increases by Rs. 100. What is the monthly salary of the manager?

Introduction / Context:
This is a simple salary average problem where the inclusion of an additional person changes the average. The question checks if you can correctly adjust totals when the average of a group changes due to one new member. Problems like these are common in basic quantitative aptitude relating to averages and money.

Given Data / Assumptions:

There are 20 employees initially.
Their average monthly salary is Rs. 1500.
When the manager joins, the average salary of the 21 people increases by Rs. 100 and becomes Rs. 1600.
We must find the salary of the manager.
All salaries are monthly and measured in rupees.

Concept / Approach:
The total salary of the initial group can be found by multiplying the average salary by the number of employees. Similarly, the total salary of the enlarged group including the manager is the new average multiplied by the new number of persons. The difference between these two totals is equal to the manager’s salary, since only that one person has been added.

Step-by-Step Solution:
Step 1: Compute total salary of the 20 employees. Total salary of 20 employees = 1500 * 20 = Rs. 30000. Step 2: Compute total salary after adding the manager. New average salary = 1500 + 100 = Rs. 1600. Number of persons now = 20 + 1 = 21. Total salary of 21 persons = 1600 * 21 = Rs. 33600. Step 3: Find the manager’s salary. Manager’s salary = total salary of 21 persons - total salary of 20 employees. Manager’s salary = 33600 - 30000 = Rs. 3600.

Verification / Alternative Check:
We can verify by taking the total salary including the manager, which is Rs. 33600, and dividing it by 21. This indeed gives 33600 / 21 = 1600, matching the new average. Removing the manager’s salary from this total leaves 30000 for 20 employees, which corresponds to the original average 1500. Thus all given conditions are satisfied by a manager’s salary of Rs. 3600.

Why Other Options Are Wrong:
Option Rs. 3700 would result in a new total of 30000 + 3700 = 33700, giving an average slightly more than Rs. 1600, which is not accepted by the question.
Option Rs. 3800 or Rs. 3900 would make the increase in average more than Rs. 100, giving averages higher than Rs. 1600, so they are incorrect.

Common Pitfalls:
A common mistake is to think the manager’s salary is simply 1600 or 1500 plus 100 without considering how averages work for groups of different sizes. Some students also forget to multiply the average by the number of persons to get totals and instead attempt short cuts that do not hold in general.

Final Answer:
The monthly salary of the manager is Rs. 3600.