Four pupils have an average age of 12years and two other pupils of average age of 10.5years are added. What is the average age of the six pupils?

Analyze the question: We are combining two groups of pupils and need the average age of the whole group. The key idea is that we cannot just average 12 and 10.5. The groups have different sizes, so we must use total ages.

Concept: Average = (Sum of all ages) ÷ (Number of pupils) So, Sum of ages = Average × Number of pupils

Solution:

1. Total age of the first 4 pupils = 4 × 12 = 48 years
2. Total age of the 2 added pupils = 2 × 10.5 = 21 years
3. Total age of all 6 pupils = 48 + 21 = 69 years
4. Average age of the 6 pupils = 69 ÷ 6 = 11.5 years

Check against the options: 11.5 years matches option C.

Tip: When groups have different sizes, use a weighted average. Turn each average back into a total (average × number), add the totals, then divide by the combined number. The answer should lie between 10.5 and 12, and closer to 12 because that group is larger. 11.5 fits this check.