The average age of 3 friends is 23 .Even if the age of the 4th friend is added , the average remains 23 . What is the age of the 4 th friend ?

Options

A. 21 years
B. 23 years
C. 32 years
D. 34 years

Answer

To find the age of the 4th friend, we can follow these steps:

### Step 1: Calculate the total age of the first three friends.
Given that the average age of the 3 friends is 23, we can use the formula for average:

\[ \text{Average} = \frac{\text{Sum of ages}}{\text{Number of friends}} \]

So, we can rearrange this to find the sum of the ages of the first three friends:

\[ \text{Sum of ages of 3 friends} = \text{Average} \times \text{Number of friends} = 23 \times 3 = 69 \]

### Step 2: Set up the equation for the total age when the 4th friend is added.
When the 4th friend is added, the average remains 23. Now, we have 4 friends, so we can set up the equation:

\[ \text{Average} = \frac{\text{Sum of ages of 4 friends}}{\text{Number of friends}} = 23 \]

Thus, the sum of the ages of the 4 friends can be expressed as:

\[ \text{Sum of ages of 4 friends} = 23 \times 4 = 92 \]

### Step 3: Find the age of the 4th friend.
Now, we know the sum of the ages of the first three friends is 69 (from Step 1), and the sum of the ages of all four friends is 92 (from Step 2). We can find the age of the 4th friend (let's call it \( x_4 \)) by subtracting the sum of the ages of the first three friends from the total sum:

\[ x_4 = \text{Sum of ages of 4 friends} - \text{Sum of ages of 3 friends} = 92 - 69 = 23 \]

### Conclusion:
The age of the 4th friend is 23.

---