Question
Download Solution PDFIn a class of 30 students, the average age is 10 years, if the age of the teacher is also included the average increases by 1, find the age of the teacher?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF
Given:
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Total number of students = 30
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Average age of students = 10 years
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Including the teacher, the average age increases by 1 year, making it 11 years.
Concept Used:
The average age of a group is calculated as:
Average = (Sum of ages) / (Number of people)
Rearranging, we get: Sum of ages = Average × Number of people
Calculation:
Step 1: Calculate the total age of the students.
Sum of ages of students = Average age × Number of students
⇒ Sum = 10 × 30
⇒ Sum = 300 years
Step 2: Calculate the total age (students + teacher).
New average = 11 years
Total number of people = 30 students + 1 teacher = 31
⇒ Total sum = New average × Total number of people
⇒ Total sum = 11 × 31
⇒ Total sum = 341 years
Step 3: Find the age of the teacher.
Age of teacher = Total sum (students + teacher) - Sum of ages of students
⇒ Age of teacher = 341 - 300
⇒ Age of teacher = 41 years
Conclusion:
∴ The age of the teacher is 41 years.
Last updated on Jul 1, 2025
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