The average age of 30 boys in a class is 15 years. If we include the age of two teachers the average age increases by 1. Find the sum of ages of the two teachers.

Options

A. A. 64 years
B. B. 62 years
C. C. 58 years
D. D. 55 years

Answer

To solve the problem step by step, we will follow these calculations:

1. **Calculate the total age of the 30 boys**:
- The average age of the boys is given as 15 years.
- The number of boys is 30.
- Total age of the boys = Average age × Number of boys = 15 years × 30 = 450 years.

2. **Determine the new average age when the two teachers are included**:
- When the ages of the two teachers are included, the average age increases by 1 year, making the new average age 16 years.

3. **Calculate the total number of individuals now**:
- The total number of individuals (boys + teachers) = 30 boys + 2 teachers = 32 individuals.

4. **Calculate the total age of all individuals including the teachers**:
- Total age with teachers = New average age × Total number of individuals = 16 years × 32 = 512 years.

5. **Find the sum of the ages of the two teachers**:
- To find the sum of the ages of the two teachers, we subtract the total age of the boys from the total age of all individuals.
- Sum of ages of the two teachers = Total age with teachers - Total age of boys = 512 years - 450 years = 62 years.

Thus, the sum of the ages of the two teachers is **62 years**.