The average age of eight teachers in a school is 40 years. A teacher among them died at the age of 55 years whereas another teacher whose age was 39 years joins them. The average age of the teachers In the school now is (in years)

Options

A. 35
B. 36
C. 38
D. 39

Answer

To find the new average age of the teachers after one teacher dies and another joins, we can follow these steps:

### Step 1: Calculate the total age of the original group of teachers.
The average age of the eight teachers is given as 40 years. To find the total age of all the teachers, we can use the formula:

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

Substituting the values:

\[ \text{Total Age} = 40 \text{ years} \times 8 = 320 \text{ years} \]

### Step 2: Adjust the total age for the teacher who died.
One teacher who was 55 years old died. We need to subtract this age from the total age calculated in Step 1:

\[ \text{New Total Age} = 320 \text{ years} - 55 \text{ years} = 265 \text{ years} \]

### Step 3: Add the age of the new teacher.
A new teacher aged 39 years joins the group. We need to add this age to the new total age:

\[ \text{Final Total Age} = 265 \text{ years} + 39 \text{ years} = 304 \text{ years} \]

### Step 4: Calculate the new average age.
Now, we need to find the new average age of the teachers. The number of teachers is now 8 - 1 + 1 = 8 (since one teacher died and one joined). We can use the formula for average again:

\[ \text{New Average Age} = \frac{\text{Final Total Age}}{\text{Number of Teachers}} \]

Substituting the values:

\[ \text{New Average Age} = \frac{304 \text{ years}}{8} = 38 \text{ years} \]

### Final Answer:
The average age of the teachers in the school now is **38 years**.

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