Explanation:

Let average age of the class was A months initially.

Total age of all students combined initially = 20 × A

Let the age of newly added boy is B months.

New average age of the class = (A – 2) months [Average decreased by 2 months]

New total age of all students combined = 20 × (A – 2) months.

∴ 20 × (A – 2) = (20 × A) – (18 × 12) + B
[18 year boy replaced by B]

⇒ – 40 = B – (216)

⇒ B = 216 – 40 = 176 months = 14 years and 8 months

Note: All ages are used in months for convenience.