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: 50 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
- 31
- 40
- 46
- 50
Show the answer and the worked solution
Correct answer: C. 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
A newcomer who raises the average of n people by d is worth (new average) + n × d — here 16 + 30 = 46. They sit at the new average and lift everyone else by d.
Shortcut. Newcomer = old average + new headcount × rise = 15 + 31 × 1 = 46.
Common trap. "31" — adding the two averages, 15 + 16, instead of comparing the totals 450 and 496.