There are 25 teacher in a school , the average age of teacher is 40. If a teacher of 60 years of age is retired than a new teacher is appointed in place of him and the average decreases to 39 . find the age of teacher appointed

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Calculate the initial total age of the teachers
Given that there are 25 teachers and the average age is 40 years, we can calculate the total age of all teachers.

\[ \text{Total age} = \text{Average age} \times \text{Number of teachers} = 40 \times 25 = 1000 \text{ years} \]

### Step 2: Account for the retirement of the 60-year-old teacher
When a teacher aged 60 retires, we need to subtract their age from the total age calculated in Step 1.

\[ \text{New total age} = 1000 - 60 = 940 \text{ years} \]

### Step 3: Add the age of the new teacher
Let the age of the new teacher be \( x \). The new total age after the new teacher is appointed will be:

\[ \text{New total age} = 940 + x \]

### Step 4: Set up the equation for the new average age
The problem states that after the new teacher is appointed, the average age decreases to 39 years. The number of teachers remains 25. Therefore, we can set up the equation:

\[ \frac{940 + x}{25} = 39 \]

### Step 5: Solve for \( x \)
To find \( x \), we first multiply both sides of the equation by 25:

\[ 940 + x = 39 \times 25 \]

Calculating \( 39 \times 25 \):

\[ 39 \times 25 = 975 \]

Now, substituting back into the equation:

\[ 940 + x = 975 \]

Next, isolate \( x \):

\[ x = 975 - 940 \]

Calculating \( 975 - 940 \):

\[ x = 35 \]

### Conclusion
The age of the new teacher appointed is **35 years**.

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