-  Avg x Number = Total
27 nos x 10 years = 270 years            ….(1)
28 nos x 11 years = 308 years            ….(2)
Teacher's age = (2) - (1) = 308 - 270 = 38 years

Let's assume the sum of ages of all 27 students to be "S". Then,

S / 27 = 10 years (Given, average age of the class is 10 years)

S = 270 years

When the teacher's age is included, the number of individuals becomes 28 and the average age becomes 11. So, we can write the following equation:

(S + T) / 28 = 11 years (T is the age of the teacher)

S + T = 308

Now, substituting the value of S from equation 1, we get

270 + T = 308

T = 38 years

Hence, the age of the teacher is 38 years (Option A).

Explanation:

• Average age of a group of individuals can be calculated by dividing the sum of ages of all individuals by the total number of individuals.
• If the average age of a group of individuals is known, we can find the sum of their ages by multiplying the average age with the total number of individuals.
• If a new individual is added to the group, the average age of the group can be found by dividing the updated sum of ages by the new total number of individuals.
• By equating the updated average age with the original average age and the updated sum of ages with the original sum of ages, we can find the age of the new individual.