Class average with replacement: In a class of 20 boys, the overall average age decreases by 2 months when one boy aged 18 years is replaced by a new entrant. Determine the exact age of the new boy (express your answer in years and months, keeping all quantities consistent and without rounding).

Introduction / Context:
Average age problems often use the relation between total sum and average. A replacement that changes the average implies a precise change in the class total. We use years as the base unit and convert months where needed.

Given Data / Assumptions:

• Number of boys = 20
• One 18 year old leaves; a new boy joins
• Average decreases by 2 months = 2/12 year = 1/6 year

Concept / Approach:
The class total equals average * count. Let initial average be A years. New average is A - 1/6. Replacement changes total by (new_boy_age - 18).

Step-by-Step Solution:

Verification / Alternative check:
Decrease in total due to average drop = 20 * (1/6) = 10/3 years, which matches 18 - 14 2/3 = 10/3 years.

Why Other Options Are Wrong:

• 15 years: Too high; would reduce total by only 3 years, not 10/3.
• 16 years 4 months: Higher still; change is smaller than required.
• 17 years 10 months: Nearly no change; incorrect.

Common Pitfalls:
Forgetting to convert months to a fraction of a year or mixing up which total increases or decreases.

Final Answer: