The average age of a class of 30 students is 12 years. If the average age of 5 of these students is 10 years and another group of 5 is 14 years, then the average age of the remaining students is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 12 years
Average \(=\) total \(\div\) number, so the totals of ages can be found and subtracted.
Total age of the class \(=30\times12=360\) years
Total age of the two groups \(=5\times10+5\times14=50+70=120\) years
Remaining students \(=30-10=20\), with total age \(360-120=240\) years
Their average \(\displaystyle =\frac{240}{20}=12\) years
Shortcut: The two groups are 2 years below and 2 years above the class average, and have 5 students each, so together they balance at 12. The rest must then also average 12 years.