There are 15 students in a class. The average age of the students and the teacher of the class is 15 years. The average age of the teacher and the students is 2 years more than that of students. What is the age of the class teacher? 

Concept Used:-

The average of the group of numbers is the ratio of the sum of all the numbers given to the total number.

The formula to found the average is given below.

⇒ Average = (sum of all the observation) / (Total number of observation)

Explanation:-

Suppose the age of the class teacher is x years.

Also, let sum of ages of students is y years.

Total students in the class = 15.

The average age of students and teacher = 15 years.

⇒ (x + y) / 16 = 15

⇒ (x + y) = 240        ....(1)

The average age of the teacher and the students is 2 years more than that of students. Thus,

⇒ (y / 15) + 2 = 15 

⇒ y =13 × 15 

⇒ y = 195

Put this value in equation (1),

⇒ (x + y) = 240

⇒ (x + 195)  = 240

⇒ x = 45 years

So, the age of the class teacher is 45 years.

Hence, the correct option is 4.