The average age of 12 players of a team is 25 yr . If the captain 's age is included, the average age incrases by 1 yr . The age of the captian is

Options

A. 25 yr
B. 38 yr
C. 36 yr
D. 26 yr

Answer

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

### Step 1: Calculate the total age of the 12 players.
The average age of the 12 players is given as 25 years. We can calculate the total age using the formula:

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

Substituting the values:

\[ \text{Total Age} = 25 \times 12 = 300 \text{ years} \]

### Step 2: Calculate the new average age when the captain is included.
When the captain's age is included, the average age increases by 1 year, making it 26 years. Now we have 13 players (12 players + 1 captain).

### Step 3: Calculate the total age of the 13 players.
Using the new average age, we can find the total age of the 13 players:

\[ \text{Total Age with Captain} = \text{New Average Age} \times \text{Total Number of Players} \]

Substituting the values:

\[ \text{Total Age with Captain} = 26 \times 13 = 338 \text{ years} \]

### Step 4: Find the age of the captain.
Now, we can find the captain's age by subtracting the total age of the 12 players from the total age of the 13 players:

\[ \text{Captain's Age} = \text{Total Age with Captain} - \text{Total Age of 12 Players} \]

Substituting the values:

\[ \text{Captain's Age} = 338 - 300 = 38 \text{ years} \]

### Final Answer:
The age of the captain is **38 years**.

---