Question 8: Average Age of New Boys In a group of 8 boys, 2 men aged 21 and 23 were...
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Question 8: Average Age of New Boys
In a group of 8 boys, 2 men aged 21 and 23 were replaced by two new boys. Due to this, the average age of the group increased by 2 years. What is the average age of the 2 new boys?
Show answer & explanation
When 2 men aged 21 and 23 (total 44 years) are replaced by 2 new boys, the average age of the 8-person group increases by 2 years. This means the total age of the group increased by 8 × 2 = 16 years. Therefore, the sum of the two new boys' ages is 44 + 16 = 60 years, giving an average of 60 ÷ 2 = 30 years.
Step-by-step Derivation:
Step 1: Calculate total age increase in the group.
Total increase = Number of boys × Increase in average = 8 × 2 = 16 years
Step 2: Calculate sum of ages of two new boys.
Sum of replaced men's ages = 21 + 23 = 44 years
Sum of new boys' ages = 44 + 16 = 60 years
Step 3: Calculate average age of two new boys.
Average = 60 ÷ 2 = 30 years
Verification: If new boys' total is 60, old men's total was 44, difference is +16 years total → +2 years per person in group of 8. ✓