The average age of 24 students and the class teacher is 16 years. If the class teacher’s age is excluded, the average reduces by one year. What is the age of the class teacher?

Options

A. 50 years
B. 45 years
C. 40 years
D. Data inadequate

Answer

To find the age of the class teacher, we can follow these steps:

### Step 1: Calculate the total age of 24 students and the class teacher.
Given that the average age of 24 students and the class teacher is 16 years, we can calculate the total age:

\[ \text{Total Age} = \text{Average Age} \times \text{Total Number of Individuals} \]
\[ \text{Total Age} = 16 \times 25 = 400 \text{ years} \]

### Step 2: Set up the equation for the average age without the class teacher.
When the class teacher's age is excluded, the average age of the 24 students becomes 15 years (since it reduces by 1 year). The total age of the 24 students can be expressed as:

\[ \text{Total Age of Students} = \text{Total Age} - \text{Age of Class Teacher} \]
Let the age of the class teacher be \( x \). Therefore, we have:

\[ \text{Total Age of Students} = 400 - x \]

### Step 3: Set up the equation for the new average.
The new average age of the 24 students is given as 15 years:

\[ \text{New Average} = \frac{\text{Total Age of Students}}{\text{Number of Students}} \]
Substituting in the values, we get:

\[ 15 = \frac{400 - x}{24} \]

### Step 4: Solve for \( x \).
To eliminate the fraction, multiply both sides by 24:

\[ 15 \times 24 = 400 - x \]
\[ 360 = 400 - x \]

Now, rearranging the equation gives:

\[ x = 400 - 360 \]
\[ x = 40 \]

### Conclusion:
The age of the class teacher is \( 40 \) years.

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