The average age of 20 students in a class is 15 yr. The teacher's age is included, the average increases by one What is the teacher's age
(a)30yr
(b)21yr
(c)42yr
(d)36yr

Options

A. 30yr
B. 21yr
C. 42yr
D. 36yr

Answer

To find the teacher's age based on the information given, we can follow these steps:

### Step 1: Calculate the total age of the 20 students
The average age of the 20 students is given as 15 years. To find the total age of these students, we use the formula:

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

Substituting the values:

\[ \text{Total Age} = 15 \times 20 = 300 \text{ years} \]

### 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, making it 16 years. Now, the total number of individuals (students + teacher) is 21.

### Step 3: Calculate the new total age with the teacher included
Using the new average age, we can calculate the new total age:

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

Substituting the values:

\[ \text{New Total Age} = 16 \times 21 = 336 \text{ years} \]

### Step 4: Calculate the teacher's age
Now, we can find the teacher's age by subtracting the total age of the students from the new total age:

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

Substituting the values:

\[ \text{Teacher's Age} = 336 - 300 = 36 \text{ years} \]

### Conclusion
The teacher's age is 36 years.