The average age of 36 students in a group is 14 years, when teacher's age is included to it, the average increases by one. What is the teacher's age in years?

Answer

To solve the problem step by step, we will follow the logic outlined in the video transcript.

### Step 1: Calculate the total age of the 36 students.
The average age of the 36 students is given as 14 years. To find the total age of all the students, we multiply the average age by the number of students.

\[ \text{Total age of 36 students} = \text{Average age} \times \text{Number of students} = 14 \times 36 \]

Calculating this gives:

\[ 14 \times 36 = 504 \text{ years} \]

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

\[ \text{New average age} = 14 + 1 = 15 \text{ years} \]

### Step 3: Calculate the total age of 37 individuals (36 students + 1 teacher).
Now, we have 36 students and 1 teacher, making a total of 37 individuals. To find the total age of these 37 individuals, we multiply the new average age by the total number of individuals.

\[ \text{Total age of 37 individuals} = \text{New average age} \times \text{Total number of individuals} = 15 \times 37 \]

Calculating this gives:

\[ 15 \times 37 = 555 \text{ years} \]

### Step 4: Calculate the teacher's age.
To find the teacher's age, we subtract the total age of the 36 students from the total age of the 37 individuals.

\[ \text{Teacher's age} = \text{Total age of 37 individuals} - \text{Total age of 36 students} = 555 - 504 \]

Calculating this gives:

\[ 555 - 504 = 51 \text{ years} \]

### Final Answer:
The teacher's age is **51 years**.

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