Two years ago, the average age of A and B was 26 years. The age of A five years from now will be 40 years, and B is 5 years younger than C. What is the difference between the present ages of A and C?

Introduction / Context:
This age problem combines an average age condition with individual future age information and an age difference involving a third person. By turning each sentence into an algebraic equation, we can systematically solve for the present ages of all three people and then compute the required difference.

Given Data / Assumptions:

• Two years ago, the average age of A and B was 26 years.
• The age of A after 5 years will be 40 years.
• B is 5 years younger than C at present.
• We need the difference between the present ages of A and C.

Concept / Approach:
First determine A's present age using the future age information. Then use the past average to find B's present age. Finally, relate B and C using the given difference and compute C's age. The answer is the absolute difference between the present ages of A and C. Linear equations and average formula are used.

Step-by-Step Solution:
Let A, B and C be their present ages in years. We are told that A + 5 = 40, so A = 40 - 5 = 35 years. Two years ago, A's age was 35 - 2 = 33 years and B's age was B - 2. The average age two years ago was 26, so (33 + (B - 2)) / 2 = 26. This gives 33 + B - 2 = 52 so B + 31 = 52. Thus B = 52 - 31 = 21 years. B is 5 years younger than C, so C = B + 5 = 21 + 5 = 26 years. Difference between present ages of A and C = 35 - 26 = 9 years.

Verification / Alternative check:
Check the average condition: two years ago A was 33 and B was 19. Their total was 52, and the average was 52 / 2 = 26, which matches. Check B and C: 21 and 26 differ by 5 years, as stated. Check A's future age: 35 + 5 = 40 years, as given. All conditions are satisfied, confirming that a 9 year difference is correct.

Why Other Options Are Wrong:
Differences such as 11, 7 or 13 years do not match when you reconstruct the ages and test the given statements. For example, if C were 24 or 28 years old, some of the equations would fail. The option 5 years would mean B and C are almost the same age as A, contradicting the calculations. Only a 9 year difference fits all the data properly.

Common Pitfalls:
Learners sometimes forget that the average two years ago involves the ages at that past time, not present ages. Another common mistake is to misinterpret "5 years younger" and subtract in the wrong direction. Carefully translating each sentence into a stepwise equation avoids these issues.

Final Answer:
So, the difference between the present ages of A and C is 9 years.