Teacher added to class: The average age of 24 students is 10 years. When the teacher is included, the average increases by 1 year. Determine the age of the teacher.
Aptitude
Average
Difficulty: Easy
Choose an option
Answer
Correct Answer: 35 years
Explanation
Introduction / Context:Adding one data point that raises the average lets us compute that data point by comparing totals before and after inclusion.Given Data / Assumptions:
- Students = 24, student average = 10 years
- With teacher, count = 25, new average = 11 years
Concept / Approach:Total = average * count. Teacher age = new total - old total.Step-by-Step Solution:
Old total = 24 * 10 = 240New total = 25 * 11 = 275Teacher age = 275 - 240 = 35 yearsVerification / Alternative check:Check average with teacher: (240 + 35)/25 = 275/25 = 11. Correct.Why Other Options Are Wrong:
- 25 or 30 years: Insufficient to raise the average by 1.
- 40 years: Would increase the average more than required for these counts.
Common Pitfalls:Mistaking the direction of change, or forgetting that adding an older person increases the total appropriately.Final Answer:
35 years