Three years ago, the average age of A and B was 18. Now, after C joins, the average of A, B, and C is 22. How old is C now?

Difficulty: Easy

24 years
27 years
28 years
30 years
None of these

Correct Answer: 24 years

Explanation:

Introduction / Context:
Average age questions translate to total-sum calculations. A known average times the number of people yields the total of their ages at that time. We compare “three years ago” and “now with a third person” to isolate C’s present age.

Given Data / Assumptions:

3 years ago: average(A, B) = 18 ⇒ sum(A, B) then = 36.
Now: average(A, B, C) = 22 ⇒ sum(A, B, C) now = 66.

Concept / Approach:
Convert averages to totals and use aging. From 3 years ago to now, A and B each gain 3 years, so the pair’s sum increases by 6. Subtract to find C’s age.

Step-by-Step Solution:

Sum(A, B) three years ago = 36.Sum(A, B) now = 36 + 3 + 3 = 42.Sum(A, B, C) now = 66 ⇒ C = 66 − 42 = 24.

Verification / Alternative check:

If A + B = 42 now, and C = 24, then average now = (42 + 24)/3 = 22 ✔.

Why Other Options Are Wrong:

27, 28, 30 do not satisfy totals/averages simultaneously.

Common Pitfalls:

Forgetting that both A and B aged 3 years each, adding 6 to the sum.Multiplying averages incorrectly instead of totals.

Three years ago, the average age of A and B was 18. Now, after C joins, the average of A, B, and C is 22. How old is C now?

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