The average age of A and B is 18 years. After 3 years, C joins them and at that time the average age of A, B, and C together becomes 22 years. What is the present age of C in years?

Introduction / Context:
This question combines the concept of average age with the idea of a new person joining the group after some years. The average age of A and B is given, and three years later C joins them, at which point the new average of all three is known. From this information, we must determine the current age of C. This type of problem is a good test of how well you can handle time shifts in average calculations.

Given Data / Assumptions:
- The average age of A and B at present is 18 years.
- This means their total present age is 2 * 18 years.
- After 3 years, C joins A and B.
- At that time, the average age of A, B, and C together is 22 years.
- Ages are measured in years.
- We need the present age of C, not C's age after 3 years.

Concept / Approach:
First we calculate the total present age of A and B using their average. After 3 years, both A and B will have aged 3 years each, so their combined age increases accordingly. When C joins them after 3 years, we use the new average to find the total age of the three at that time. Subtracting the future total age of A and B from this combined total gives C's age at that time, and then we subtract 3 years to get C's present age.

Step-by-Step Solution:
Step 1: Total present age of A and B is 2 * 18 = 36 years.Step 2: After 3 years, A and B will both be 3 years older. Their total age at that time will be 36 + 3 + 3 = 42 years.Step 3: When C joins them after 3 years, there are 3 people with an average age of 22 years.Step 4: Total age of A, B, and C at that time is 3 * 22 = 66 years.Step 5: Therefore, C's age at that time is 66 - 42 = 24 years.Step 6: Since this is C's age after 3 years, C's present age is 24 - 3 = 21 years.

Verification / Alternative check:
Assume C is currently 21 years old. After 3 years, C will be 24 years old. If the total age of A and B at present is 36 years, after 3 years their total will be 42 years. Adding C's age of 24 years at that time gives 42 + 24 = 66 years. Dividing by 3 people gives an average of 22 years, which matches the problem statement. This confirms that C's present age is indeed 21 years.

Why Other Options Are Wrong:
If C were 20, 23, 24, or 27 years old at present, then C's age after 3 years would be 23, 26, 27, or 30 years. When we add any of these to the future total age of A and B, the combined total age would not be 66, and the average would not be exactly 22 years. Thus, those options violate the conditions given in the question.

Common Pitfalls:
The most common mistake is to treat 22 years as the present average instead of the average after 3 years. Another error is failing to increase the ages of A and B by 3 years before forming the equation with the new average. Some learners also try to treat C's present age and C's age after 3 years as the same, which is incorrect. Carefully separating present and future ages is essential.

Final Answer:
The present age of C is 21 years.