The average age of a class of 39 students Is 15 years. If the age of the teacher is included, then the average increases by 3 months. Find the age of the teacher.

Options

A. 30 years
B. 25 years
C. 35 years
D. 40 years

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Calculate the total age of the 39 students.
The average age of the class is given as 15 years. To find the total age of the 39 students, we can use the formula:

\[ \text{Total Age of Students} = \text{Average Age} \times \text{Number of Students} \]

Substituting the values:

\[ \text{Total Age of Students} = 15 \text{ years} \times 39 = 585 \text{ years} \]

### Step 2: Understand the effect of including the teacher's age.
When the teacher's age is included, the average age increases by 3 months. Since there are 12 months in a year, 3 months is equivalent to:

\[ \text{Increase in Average Age} = \frac{3}{12} \text{ years} = 0.25 \text{ years} \]

Thus, the new average age becomes:

\[ \text{New Average Age} = 15 \text{ years} + 0.25 \text{ years} = 15.25 \text{ years} \]

### Step 3: Calculate the total age of the class including the teacher.
Now, we need to calculate the total age of the class including the teacher. The total number of individuals (students + teacher) is 40. Therefore, we can find the total age as follows:

\[ \text{Total Age with Teacher} = \text{New Average Age} \times \text{Total Number of Individuals} \]

Substituting the values:

\[ \text{Total Age with Teacher} = 15.25 \text{ years} \times 40 = 610 \text{ years} \]

### Step 4: Find the age of the teacher.
Now, we can find the age of the teacher by subtracting the total age of the students from the total age including the teacher:

\[ \text{Age of Teacher} = \text{Total Age with Teacher} - \text{Total Age of Students} \]

Substituting the values:

\[ \text{Age of Teacher} = 610 \text{ years} - 585 \text{ years} = 25 \text{ years} \]

### Final Answer:
The age of the teacher is **25 years**.

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