Averages — “Ten years ago, the average age of A and B was 20. Today, the average age of A, B, and C is 30. How old will C be after 5 years?”

Introduction / Context:
This average problem uses time shifts. We reconstruct past and present totals from averages, then isolate C’s current age and project forward by 5 years.

Given Data / Assumptions:

• 10 years ago: average(A,B) = 20 ⇒ sum(A,B) then = 40.
• Today: sum(A,B) = 40 + 2*10 (both aged 10 more) = 60.
• Today: average(A,B,C) = 30 ⇒ sum(A,B,C) = 90.
• Therefore C today = 90 − 60.

Concept / Approach:
Translate averages to totals, adjust totals across time correctly for each person, and subtract to isolate C. Finally, add 5 years to get C’s age after 5 years.

Step-by-Step Solution:

Verification / Alternative check:
Recheck totals: If A + B = 60 and C = 30 today, average is (60 + 30)/3 = 30 as given. Consistent.

Why Other Options Are Wrong:
20/30/55/25 do not match the derived present age (30) advanced by 5 years.

Common Pitfalls:
Forgetting to increase both A and B by 10 to move from past to present; averaging 20 and 30 directly; or miscounting the number of persons while forming totals.

Final Answer:
35 years