The average age of a group of 25 girls is 10year. If one girl, aged 12 years and 4 months joins the group, find the new average age of the group

Analyze the question: We have 25 girls with an average age of 10 years. One more girl, aged 12 years 4 months, joins. We need the new average for 26 girls.

Concept: Average = (Sum of all ages) ÷ (Number of people). So the sum of ages = average × number.

Solution:

1. Convert the new girl's age to years: 12 years 4 months = 12 + 4/12 = 12⅓ ≈ 12.333 years.

2. Original total age = 25 × 10 = 250 years.

3. New total age = 250 + 12.333 = 262.333 years.

4. New number of girls = 26.

5. New average = 262.333 ÷ 26 ≈ 10.09 years ≈ 10.1 years (to 1 decimal place).

Check: The new girl is older than the current average, so the average must go up slightly from 10. Only option A (10.1) is above 10, and options B, C, and D are all below 10, so they are impossible.

Correct answer: A. 10.1 years

Tip: Before calculating, ask yourself whether the new member is older or younger than the current average. If older, the average rises. If younger, it falls. This often lets you eliminate wrong options instantly. Also, always convert months to a fraction of a year (months ÷ 12).