A cricketer scored some runs in his continuous 9 innings. He scored 100 runs in his 10th innings and increases his average by 8 runs. What was the average of his runs at the end of 10th innings?

Options

A. 20
B. 24
C. 28
D. 32

Answer

To solve the problem, we need to find the average runs scored by the cricketer at the end of his 10th innings. Let's break it down step by step.

### Step 1: Define Variables
Let the average runs scored in the first 9 innings be \( x \).

### Step 2: Calculate Total Runs for First 9 Innings
The total runs scored in the first 9 innings can be expressed as:
\[ \text{Total runs in 9 innings} = 9x \]

### Step 3: Add Runs from the 10th Innings
The cricketer scored 100 runs in the 10th inning. Therefore, the total runs after 10 innings becomes:
\[ \text{Total runs in 10 innings} = 9x + 100 \]

### Step 4: Calculate New Average After 10 Innings
The average after 10 innings can be calculated as:
\[ \text{New average} = \frac{9x + 100}{10} \]

### Step 5: Set Up the Equation for Average Increase
According to the problem, the new average is 8 runs more than the previous average:
\[ \frac{9x + 100}{10} = x + 8 \]

### Step 6: Solve the Equation
To solve for \( x \), we first multiply both sides by 10 to eliminate the fraction:
\[ 9x + 100 = 10(x + 8) \]
Expanding the right side gives:
\[ 9x + 100 = 10x + 80 \]
Now, rearranging the equation:
\[ 100 - 80 = 10x - 9x \]
\[ 20 = x \]

### Step 7: Calculate the New Average
Now that we have \( x \), which is the average after 9 innings, we can find the new average:
\[ \text{New average} = x + 8 = 20 + 8 = 28 \]

### Conclusion
Thus, the average of his runs at the end of the 10th innings is:
\[ \boxed{28} \]