The average age of 3 friends is 23 years. Even if the age of 4th friend Is added, the average age remains the same. Then the age of the fourth friend is :

Options

A. 20 years
B. 21 years
C. 22 years
D. 23 years

Answer

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

### Step 1: Calculate the total age of the first three friends.
The average age of the three friends is given as 23 years. The formula for average is:

\[ \text{Average} = \frac{\text{Total Sum of Ages}}{\text{Number of Friends}} \]

Let the total age of the three friends be \( S_3 \). Therefore, we can express this as:

\[ 23 = \frac{S_3}{3} \]

Multiplying both sides by 3 gives:

\[ S_3 = 23 \times 3 = 69 \text{ years} \]

### Step 2: Set up the equation for the total age of four friends.
When the fourth friend is added, the average age remains 23 years. Now, the total number of friends is 4. Let the age of the fourth friend be \( x \). The total age of the four friends can be expressed as:

\[ S_4 = S_3 + x = 69 + x \]

Using the average formula again for four friends:

\[ 23 = \frac{S_4}{4} \]

Substituting \( S_4 \):

\[ 23 = \frac{69 + x}{4} \]

### Step 3: Solve for the age of the fourth friend.
To eliminate the fraction, multiply both sides by 4:

\[ 92 = 69 + x \]

Now, isolate \( x \):

\[ x = 92 - 69 \]
\[ x = 23 \text{ years} \]

### Conclusion
The age of the fourth friend is **23 years**.

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