The average age of a group of 35 students is 15 years. If a teacher is included in the group, then the average age increases by 2 months. The age of the teacher (in years) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 21
An average times the number of people gives the total of their ages; the teacher’s age is the rise in that total when the teacher joins.
Total age of the 35 students \(=35\times15=525\) years
New average \(\displaystyle =15+\frac{2}{12}=15\frac{1}{6}\) years, for 36 people
New total \(\displaystyle =36\times15\frac{1}{6}=540+6=546\) years
Teacher’s age \(=546-525=21\) years
Shortcut: The teacher’s age is the old average plus the rise shared by everyone in the new group.
Rise for 36 people \(\displaystyle =36\times\frac{2}{12}=6\) years
Teacher’s age \(=15+6=21\) years