The average age of 27 students of a class is 22. If the age of the teacher is also added to their ages, the average increases by one. Find the age of the teacher.
A 42 B. 48 C. 50 D. 52

Options

A. C
B. A
C. D
D. B

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the total age of the 27 students.
The average age of the 27 students is given as 22. The formula for average is:

\[ \text{Average} = \frac{\text{Sum of observations}}{\text{Total number of observations}} \]

Using this formula, we can find the sum of the ages of the students:

\[ \text{Sum of ages of students} = \text{Average} \times \text{Number of students} = 22 \times 27 = 594 \]

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

\[ \text{New average} = 22 + 1 = 23 \]

Now, the total number of individuals (students + teacher) becomes:

\[ \text{Total number of individuals} = 27 + 1 = 28 \]

### Step 3: Calculate the total age of the students and the teacher combined.
Using the new average, we can find the total age of the 28 individuals (students + teacher):

\[ \text{Total age of students and teacher} = \text{New average} \times \text{Total number of individuals} = 23 \times 28 = 644 \]

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

\[ \text{Age of teacher} = \text{Total age of students and teacher} - \text{Sum of ages of students} = 644 - 594 = 50 \]

### Conclusion:
The age of the teacher is **50**.

### Answer:
C. 50

---