The average age of 24 boys and a teacher is 15. When the teacher's age is excluded the average decreases by 1 . What is the age of the teacher ?

Options

A. 39 years
B. 38 years
C. 40 years
D. 41 years

Answer

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

### Step 1: Calculate the total age of 24 boys and the teacher.
Given that the average age of 24 boys and a teacher is 15 years, we can calculate the total age of all 25 individuals (24 boys + 1 teacher).

\[ \text{Total age} = \text{Average age} \times \text{Number of individuals} \]
\[ \text{Total age} = 15 \times 25 = 375 \text{ years} \]

### Step 2: Calculate the new average age when the teacher is excluded.
When the teacher's age is excluded, the average age of the 24 boys decreases by 1 year. Therefore, the new average age of the boys is:

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

### Step 3: Calculate the total age of the 24 boys.
Now, we can calculate the total age of the 24 boys using the new average:

\[ \text{Total age of boys} = \text{New average age} \times \text{Number of boys} \]
\[ \text{Total age of boys} = 14 \times 24 = 336 \text{ years} \]

### Step 4: Calculate the age of the teacher.
Now that we have the total age of all individuals and the total age of the boys, we can find the age of the teacher by subtracting the total age of the boys from the total age of all:

\[ \text{Age of teacher} = \text{Total age} - \text{Total age of boys} \]
\[ \text{Age of teacher} = 375 - 336 = 39 \text{ years} \]

### Final Answer:
The age of the teacher is **39 years**.

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