There is group of 8 teachers. One teacher leaves the group and a new teacher joins the group. Due to this, the average age of teachers becomes same as the average 2 years ago. If the member who left was aged 42. Then what is the age (in years) of new teacher?

Options

A. 22
B. 28
C. 24
D. 26

Answer

To solve the problem step by step, let's denote the average age of the 8 teachers currently as \( A \).

### Step 1: Calculate the total age of the 8 teachers now
The total age of the 8 teachers now can be expressed as:
\[ \text{Total age now} = 8A \]

### Step 2: Determine the total age of the teachers 2 years ago
Two years ago, each teacher was 2 years younger, so the total age of the 8 teachers at that time was:
\[ \text{Total age 2 years ago} = 8(A - 2) = 8A - 16 \]

### Step 3: Account for the teacher who left
When the teacher aged 42 leaves, the total age of the remaining 7 teachers becomes:
\[ \text{Total age after leaving} = 8A - 42 \]

### Step 4: Add the new teacher's age
Let the age of the new teacher be \( x \). The total age after the new teacher joins becomes:
\[ \text{Total age after new teacher joins} = 8A - 42 + x \]

### Step 5: Set the new average age equal to the average age from 2 years ago
According to the problem, the average age after the new teacher joins is equal to the average age 2 years ago:
\[ \frac{8A - 42 + x}{8} = A - 2 \]

### Step 6: Multiply both sides by 8 to eliminate the fraction
\[ 8A - 42 + x = 8(A - 2) \]

### Step 7: Expand the right side
\[ 8A - 42 + x = 8A - 16 \]

### Step 8: Simplify the equation
Now, we can simplify the equation:
\[ -42 + x = -16 \]

### Step 9: Solve for \( x \)
Add 42 to both sides:
\[ x = 42 - 16 \]
\[ x = 26 \]

### Conclusion
The age of the new teacher is \( 26 \) years.

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