Single correct option
The average age of 30 students in a class is 15 years. When the teacher's age is included, the average rises by 6 months. If the teacher is then replaced by the headmaster, the average (of the 31 people) rises by a further 6 months. What is the headmaster's age?
- A. 45 years
- B. 46 years
- C. 30.5 years
- D. 47.5 years
Show answer and solution
Answer: (B) 46 years
Total of students = 30 × 15 = 450.
With the teacher, 31 people average 15.5, total 480.5, so the teacher is 480.5 − 450 = 30.5 years.
Replacing the teacher by the headmaster raises the average of 31 people by 0.5, so the total rises by 31 × 0.5 = 15.5. Headmaster = 30.5 + 15.5 = 46 years.
Shortcut: newcomer = old average + (group size after joining × increase) = 15 + 31 × 0.5.
With the teacher, 31 people average 15.5, total 480.5, so the teacher is 480.5 − 450 = 30.5 years.
Replacing the teacher by the headmaster raises the average of 31 people by 0.5, so the total rises by 31 × 0.5 = 15.5. Headmaster = 30.5 + 15.5 = 46 years.
Shortcut: newcomer = old average + (group size after joining × increase) = 15 + 31 × 0.5.
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