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The average age of 15 students in a class is 22 years. If the age of the teacher is included, the average increases by 1 year. What is the age of the teacher?
36 years
38 years
40 years
42 years
38 years
Add the product of the new total number of persons (16) and the increase in average (1) to the original average: 22+(16×1)=38 years.
Number of students = 15, Average age of students = 22 years, New average with teacher included = 23 years
Ageteacher=(N+1)×Anew−N×Aold
Add the product of the new total number of persons (16) and the increase in average (1) to the original average: 22+(16×1)=38 years.
Many students mistakenly add only the increase in average to the original age or forget to multiply the increased average by the new total count of people.
Calculate total age of students
Multiply the number of students by their average age to find the sum of their ages.
Total age of 15 students=15×22=330
Calculate total age including the teacher
With the teacher included, the total number of people becomes 16 and the average increases by 1 to 23 years.
Total age of 16 persons=16×23=368
Determine the age of the teacher
Subtract the total age of the 15 students from the total age of all 16 individuals.
Age of teacher=368−330=38 years
B is correct because the calculated age of the teacher is 38 years.
The balance or deviation concept used here is very helpful for solving weighted average, mixtures, and alligation problems quickly.
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