The average age of a teacher and three students is 20 years. If all the three students are of same age and the difference between the age of the teacher and each student is 20 years, then what is the age of the teacher?

The correct option is 35 years.

Step-by-Step Explanation:

1. Understand the given data:

There is 1 teacher and 3 students (total 4 people).

The average age of these 4 people is 20 years.

All three students are of the exact same age.

The difference between the age of the teacher and each student is 20 years.

2. Set up the equations:

Let the age of each student be S years.

Since the teacher is 20 years older than each student, the age of the teacher is:

$T=S+20$

3. Calculate the total age of all 4 people:

Total number of individuals = 1 teacher + 3 students = 4

Total age = Average age × Number of people

$\text{Total age}=20\times 4=80\text{years}$

4. Formulate the sum equation:

The sum of the ages of the teacher and the 3 students equals the total age:

$T+S+S+S=80$

$T+3S=80$

5. Solve for the student's age (S):

Substitute $T=S+20$ into the equation:

$(S+20)+3S=80$

$4S+20=80$

$4S=80-20$

$4S=60$

$S=\frac{60}{4}=15\text{years}$

6. Find the teacher's age (T):

$T=S+20$

$T=15+20=35\text{years}$

Thus, the age of the teacher is 35 years.