The average age of 26 students of a class is 26 years. If the age of the teacher is also included, the average age of the whole group becomes 27 years. The age (in years) of the teacher is:

Correct Answer: 53

Step-by-Step Explanation:

Step 1: Calculate the total age of the 26 students

We are given that the average age of 26 students is 26 years.

The formula for average is:

$\text{Average}=\frac{\text{Total Age}}{\text{Number of People}}$

Therefore, the total age of the 26 students can be calculated as:

$\text{Total age of 26 students}=26\times 26=676\text{years}$

Step 2: Calculate the total age including the teacher

When the teacher's age is included, the total number of people becomes 26 + 1 = 27 people.

The new average age becomes 27 years.

Now, we find the total age of the group including the teacher:

$\text{Total age of 27 people}=27\times 27=729\text{years}$

Step 3: Calculate the age of the teacher

The age of the teacher is the difference between the new total age and the original total age of the 26 students:

$\text{Age of the teacher}=729-676=53\text{years}$

Thus, the age of the teacher is 53 years.