The average of runs scored by a cricketer in his 99 innings is 99. How many runs will he have to score in his 100th Innings so that his average of runs in 100 innings may be 100?

Options

A. 100
B. 99
C. 199
D. 101

Answer

To solve the problem step by step, we will follow the logic laid out in the video transcript.

### Step 1: Understand the given information
The average runs scored by the cricketer in 99 innings is 99.

### Step 2: Calculate the total runs scored in 99 innings
To find the total runs scored in 99 innings, we can use the formula for average:
\[ \text{Average} = \frac{\text{Total Runs}}{\text{Number of Innings}} \]
Given that the average is 99 and the number of innings is 99, we can rearrange the formula to find the total runs:
\[ \text{Total Runs} = \text{Average} \times \text{Number of Innings} = 99 \times 99 = 9801 \]

### Step 3: Set up the equation for the 100th inning
Let \( x \) be the runs scored in the 100th inning. The total runs after 100 innings will then be:
\[ \text{Total Runs in 100 Innings} = 9801 + x \]

### Step 4: Calculate the desired average for 100 innings
We want the average after 100 innings to be 100. Using the average formula again:
\[ \text{Average} = \frac{\text{Total Runs in 100 Innings}}{100} \]
Setting the average to 100 gives us:
\[ 100 = \frac{9801 + x}{100} \]

### Step 5: Solve for \( x \)
To eliminate the fraction, multiply both sides by 100:
\[ 10000 = 9801 + x \]
Now, isolate \( x \):
\[ x = 10000 - 9801 = 199 \]

### Conclusion
The cricketer will need to score **199 runs** in his 100th inning to achieve an average of 100 over 100 innings.