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The average age of 5 students is 20 years. If a teacher is included, the average increases by 2. What is the age of the teacher?
30
32
34
36
32
New Average + (Number of new members × Increase in average) = 22+(6×2)=22+10=32.
Initial number of students = 5, Average age of students = 20 years, Increase in average when teacher is included = 2
Ageteacher=New Sum−Old Sum
New Average + (Number of new members × Increase in average) = 22+(6×2)=22+10=32.
Forgetting to multiply the increase in average by the total new number of members (6 persons) instead of the old number of students.
Calculate total age of 5 students
Multiply the number of students by their average age: 5×20=100 years.
TotalAge5=5×20=100
Calculate total age including the teacher
With the teacher included, total members = 5+1=6, and the new average increases by 2 to become 20+2=22 years.
TotalAge6=6×(20+2)=6×22=132
Find the age of the teacher
Subtract the total age of the 5 students from the total age of 6 persons: 132−100=32 years.
Ageteacher=132−100=32
B is correct because the age of the teacher is calculated as 32 years.
This concept of weighted averages and changes in mean is frequently tested in data interpretation and mixture-alligation problems.
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