Question : The average age of 10 students and their class teacher is 17 years. If the age of the class teacher is excluded, the average age of the 10 students is reduced by 2 years. What is the age of the class teacher?
Option 1: 38 years
Option 2: 36 years
Option 3: 37 years
Option 4: 35 years
Correct Answer: 37 years
Solution :
The average age of 10 students and their class teacher = 17 years
Sum of age of 10 students and the teacher = $17\times(10 + 1) = 187$ years
If the age of the class teacher is excluded, the average age of the 10 students is reduced by 2 years.
Thus, the total age of 10 students = $10\times(17 - 2) = 150$
$\therefore$ Age of the class teacher = $187 - 150 = 37$
Hence, the correct answer is 37 years.
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