The average age of eleven cricket players is 20 years. If the age of the coach is also Included, the average age increases by 10%. The age of the coach is:

Options

A. 48 years
B. 44 years
C. 40 years
D. 36 years

Answer

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

### Step 1: Calculate the total age of the 11 cricket players.
The average age of the 11 cricket players is given as 20 years. The formula for average is:

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

So, we can rearrange the formula to find the sum of ages:

\[ \text{Sum of ages} = \text{Average} \times \text{Number of players} \]

Substituting the values:

\[ \text{Sum of ages} = 20 \times 11 = 220 \text{ years} \]

### Step 2: Determine the new average age when the coach is included.
The problem states that including the coach increases the average age by 10%. Therefore, we calculate the new average:

\[ \text{New average} = \text{Old average} + 10\% \text{ of Old average} \]

Calculating 10% of the old average (20 years):

\[ 10\% \text{ of } 20 = 2 \]

Thus, the new average is:

\[ \text{New average} = 20 + 2 = 22 \text{ years} \]

### Step 3: Calculate the total age of the 12 individuals (11 players + 1 coach).
Now, with the coach included, the number of individuals is 12. We can find the total age of all 12 individuals using the new average:

\[ \text{Total age} = \text{New average} \times \text{Number of individuals} \]

Substituting the values:

\[ \text{Total age} = 22 \times 12 = 264 \text{ years} \]

### Step 4: Find the age of the coach.
To find the age of the coach, we subtract the total age of the 11 players from the total age of the 12 individuals:

\[ \text{Age of the coach} = \text{Total age of 12 individuals} - \text{Sum of ages of 11 players} \]

Substituting the values:

\[ \text{Age of the coach} = 264 - 220 = 44 \text{ years} \]

Thus, the age of the coach is **44 years**.

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