The ages of 10 students and their teacher are such that the average of the…
2025
The ages of 10 students and their teacher are such that the average of the first 7 students' age is 15 years; the average of the last three students' age is 11 years. The average age of all the students and their teacher together is 15 years. Find the age of the teacher.
- A.
24 years
- B.
27 years
- C.
30 years
- D.
33 years
Attempted by 7 students.
Show answer & explanation
Correct answer: B
Concept: When the average age of a group is known, the total age of that group equals average × number of members. To find one individual's age within a larger combined group, first find the total age of the combined group from its average, then subtract the total ages of every other subgroup whose average is separately known.
The combined group has 10 students + 1 teacher = 11 people. Their average age is 15 years, so the total age of this group = 11 × 15 = 165 years.
The average age of the first 7 students is 15 years, so their total age = 7 × 15 = 105 years.
The average age of the last 3 students is 11 years, so their total age = 3 × 11 = 33 years.
Total age of all 10 students = 105 + 33 = 138 years.
Age of the teacher = total age of the 11-member group − total age of the 10 students = 165 − 138 = 27 years.
Cross-check: Combined total = 138 (students) + 27 (teacher) = 165; 165 ÷ 11 = 15, which matches the given overall average — confirming the result.