A cricketer has completed 10 innings and his average is 21.5 runs. How many runs must he take in next innings so as to raise his average by 24?

Let's solve this step by step.

### Given:
- The cricketer has completed 10 innings.
- His current average is 21.5 runs.
- He wants to increase his average by 24 runs, i.e., new average will be \( 21.5 + 24 = 45.5 \) runs after 11 innings.

### Step 1: Total runs after 10 innings
The average runs after 10 innings is 21.5. So, the total runs scored after 10 innings is:
\[
\text{Total runs after 10 innings} = 10 \times 21.5 = 215 \text{ runs.}
\]

### Step 2: Total runs after 11 innings (new average)
After the 11th innings, the new average is 45.5. Therefore, the total runs scored after 11 innings must be:
\[
\text{Total runs after 11 innings} = 11 \times 45.5 = 500.5 \text{ runs.}
\]

### Step 3: Runs needed in the 11th innings
To find how many runs the cricketer must score in his next innings, we subtract the total runs after 10 innings from the total runs after 11 innings:
\[
\text{Runs needed in the 11th innings} = 500.5 - 215 = 285.5.
\]

Therefore, the cricketer needs to score **285.5 runs** in his next (11th) innings to raise his average by 24 runs.

### Clarification:
Since it's unrealistic for a cricketer to score half a run, we could infer that the problem might involve rounding considerations or a simpler interpretation. However, mathematically, the answer is 285.5 runs.

Would you like further details on this or any clarifications?

### Related Questions:
1. How is batting average calculated in cricket?
2. What effect does scoring 0 in an innings have on the average?
3. If the cricketer's target average was 50 instead of 45.5, how many runs would he need to score?
4. What if the cricketer had completed 15 innings with an average of 30? How would the answer change?
5. How does the law of large numbers apply to a cricketer's batting average?

### Tip:
When dealing with averages, multiplying the average by the number of observations gives the total sum, which is useful in reverse calculations like this one.

A cricketer has completed 10 innings and his average is 21.5 runs. How many runs must he take in the next innings so as to raise his average by 24?

Learn how to calculate the number of runs a cricketer needs to score in order to increase his average by 24 runs. This problem covers key concepts of averages, basic arithmetic operations, and linear equations. Suitable for students in Grades 7-9.

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