The teacher joins the class — Averages Aptitude Question
The teacher joins the class: The average age of 30 students is 15 years. When the teacher's age is included, the… Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
The average age of 30 students is 15 years. When the teacher's age is included, the average becomes 16. How old is the teacher?
Options
- 45
- 46
- 47
- 48
Show the answer and the worked solution
Correct answer: B. 46
Worked solution
- Total age of students = 30 × 15 = 450.
- Total with the teacher = 31 × 16 = 496.
- Teacher = 496 − 450 = 46.
Answer: 46.
The idea
Shortcut: a newcomer who raises the average of n people by d is worth (new average) + n × d — here 16 + 30 × 1 = 46. The newcomer lifts everyone else by d and is themselves at the new average.
Shortcut. Teacher = old average + (n + 1) × rise = 15 + 31 × 1 = 46.
Common trap. 45 — 15 + 30 × 1, which lifts the 30 students but forgets that the teacher also sits at the new average of 16.