A teacher among the students — Aptitude Question
A teacher among the students: The average age of a class of 24 students is 16 years. If the teacher's age is… Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
The average age of a class of 24 students is 16 years. If the teacher's age is included, the average rises by 1 year. What is the teacher's age?
Options
- 31
- 36
- 41
- 45
Show the answer and the worked solution
Correct answer: C. 41
Worked solution
- Students' total = 24 × 16 = 384.
- Total with teacher = 25 × 17 = 425.
- Teacher = 425 − 384 = 41.
Answer: 41.
The idea
New average + old count × rise = 17 + 24 = 41. The newcomer sits at the new average and lifts every existing member by the increase.
Shortcut. Teacher = old average + new headcount × rise = 16 + 25 × 1 = 41: the teacher matches the old average and then adds a year for each of the 25 people now counted.
Common trap. 36 looks like a plausible teacher's age, 20 years above the students, but it lifts the average by only 20 ÷ 25 = 0.8 year; a full year needs 25 years above 16.