There 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?

The correct option is 45.

Let us break down the problem step-by-step to find the age of the class teacher.

Step 1: Understand the given information
We are given that:
1. There are 15 students in the class.
2. The average age of the students and the teacher combined is 15 years.
3. The average age of the teacher and the students (which is the combined average, 15 years) is 2 years more than the average age of the students alone.

Step 2: Find the average age of the students
Let $S$ be the average age of the students.
We are told that the combined average age of the students and the teacher is 2 years more than $S$.
Combined average = $S+2$
Since the combined average is 15 years:
$S+2=15$
Subtracting 2 from both sides, we get:
$S=13$
So, the average age of the 15 students is 13 years.

Step 3: Calculate the total age of the students
The total age of the 15 students is the number of students multiplied by their average age:
Total age of students = $15\times 13=195$ years.

Step 4: Calculate the total age of the students and the teacher combined
There are 15 students and 1 teacher, making a total of 16 people.
Their combined average age is 15 years.
Combined total age = $16\times 15=240$ years.

Step 5: Calculate the age of the class teacher
The age of the teacher is the difference between the combined total age and the total age of the students:
Age of the teacher = Combined total age - Total age of students
Age of the teacher = $240-195=45$ years.

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