The average monthly salary of 19 members of a group is Rs. 16,000. If one more member, whose monthly salary is Rs. 20,000, joins the group, what will be the new average monthly salary of the group?

Introduction / Context:
This question demonstrates how the average changes when a new data point is added to a group. We know the original average salary of 19 members and the salary of a new member who joins. Using this, we need to find the new average salary for the entire group of 20 members.

Given Data / Assumptions:

• Number of members initially = 19.
• Average monthly salary of these 19 members = Rs. 16,000.
• One more member with monthly salary Rs. 20,000 joins.
• We assume salaries are in rupees per month.

Concept / Approach:
The key idea is that:

• Total salary of a group = average salary * number of members.
• When a new member joins, new total salary = old total salary + new member salary.
• New average = new total salary / new number of members.

We will compute the original total salary, add the new salary, and then divide by 20 to get the new average.

Step-by-Step Solution:
Step 1: Compute the original total salary of 19 members. Original total = 16,000 * 19. 16,000 * 19 = 16,000 * (20 - 1) = 320,000 - 16,000 = Rs. 304,000. Step 2: Add the salary of the new member. New member salary = Rs. 20,000. New total salary = 304,000 + 20,000 = Rs. 324,000. Step 3: Compute new number of members. New number of members = 19 + 1 = 20. Step 4: Compute new average salary. New average = 324,000 / 20 = Rs. 16,200.

Verification / Alternative check:
We can see that the new member earns Rs. 4,000 more than the original average (20,000 versus 16,000). This extra Rs. 4,000 is spread across 20 members, so the average increase per member is 4,000 / 20 = Rs. 200. Therefore the new average should be 16,000 + 200 = Rs. 16,200, which matches the computed value.

Why Other Options Are Wrong:
An average of Rs. 18,250 or Rs. 18,000 would require a much larger total salary than 324,000. An average of Rs. 16,250 corresponds to a total of 325,000, which is not the correct total. Only Rs. 16,200 corresponds exactly to the new total salary of Rs. 324,000 divided by 20 members.

Common Pitfalls:
Students sometimes mistakenly average 16,000 and 20,000 directly, which ignores that there are 19 members at 16,000 and only one at 20,000. Others forget to convert averages into total sums before combining groups. The correct procedure is always to calculate the total from the original average, add the new value, and then divide by the new count.

Final Answer:
The new average monthly salary of the group is Rs. 16,200.