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?

The current average of the cricketer is 21.5 runs over 10 innings. He wants to raise his average by 24 runs, so the new average should be:

\[
21.5 + 24 = 45.5 \text{ runs}.
\]

Let's denote the total runs the cricketer has scored so far by \( T \). Since his current average is 21.5 runs over 10 innings, we can write:

\[
T = 21.5 \times 10 = 215 \text{ runs}.
\]

Let \( x \) be the number of runs he must score in the next innings to raise his average to 45.5. After this next innings, he will have played 11 innings, so his new average will be:

\[
\text{New Average} = \frac{T + x}{11}.
\]

Substituting the value of the new average:

\[
45.5 = \frac{215 + x}{11}.
\]

Now, solve for \( x \):

\[
45.5 \times 11 = 215 + x,
\]
\[
500.5 = 215 + x,
\]
\[
x = 500.5 - 215 = 285.5.
\]

Therefore, the cricketer must score **285.5 runs** in the next innings to raise his average to 45.5 runs.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to expand your understanding:
1. What would his average be if he scored fewer runs, say 100, in the next innings?
2. How is the average affected if the number of innings increases significantly?
3. What is the formula for calculating average in general?
4. How many innings would he need to play to raise his average by 10 instead of 24?
5. How would the scenario change if his current average was higher, say 30?

**Tip**: Always verify calculations when dealing with averages, as a small mistake can significantly affect the result.

Learn how to calculate the number of runs a cricketer must score in his next innings to raise his average by 24 runs. This problem involves key mathematical concepts such as averages and algebra, and is suitable for students in Grades 6-8.

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