The average age of 30 students is 15 years. If the teacher's age is also included then the average age increases by 1 year. The age of the teacher is

Options

A. A) 56 years
B. B) 46 years
C. C) 35 years
D. D) 45 years

Explanation

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

### Step 1: Calculate the total age of the 30 students.
The average age of the 30 students is given as 15 years. To find the total age of the students, we use the formula:

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

Substituting the values:

\[ \text{Total Age of Students} = 30 \times 15 = 450 \text{ years} \]

### Step 2: Determine the new average age when the teacher is included.
When the teacher's age is included, the average age increases by 1 year, making the new average age:

\[ \text{New Average Age} = 15 + 1 = 16 \text{ years} \]

### Step 3: Calculate the total age of the 31 individuals (30 students + 1 teacher).
Now, we need to find the total age of the 31 individuals (30 students + the teacher). We use the new average age to find this total:

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

Substituting the values:

\[ \text{Total Age of Students and Teacher} = 31 \times 16 = 496 \text{ years} \]

### Step 4: Find the teacher's age.
To find the teacher's age, we subtract the total age of the students from the total age of the students and the teacher:

\[ \text{Teacher's Age} = \text{Total Age of Students and Teacher} - \text{Total Age of Students} \]

Substituting the values:

\[ \text{Teacher's Age} = 496 - 450 = 46 \text{ years} \]

### Final Answer:
The age of the teacher is **46 years**.

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