The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?

Let the total runs scored by the cricket player in the first 10 innings be \( T \). According to the problem, the average of these 10 innings is 32. Thus, we have:

\[
\frac{T}{10} = 32
\]

Multiplying both sides by 10, we get:

\[
T = 320
\]

Now, let the number of runs the player needs to score in the next (11th) innings be \( x \). The new average after 11 innings should be 32 + 4 = 36. So, the equation for the new average becomes:

\[
\frac{T + x}{11} = 36
\]

Substituting \( T = 320 \) into this equation:

\[
\frac{320 + x}{11} = 36
\]

Multiplying both sides by 11:

\[
320 + x = 396
\]

Now, solving for \( x \):

\[
x = 396 - 320
\]

\[
x = 76
\]

Thus, the player must score **76 runs** in the next innings to increase the average by 4.

Do you want more details or have any questions?

Here are some related questions:
1. How would the required runs change if the player wanted to increase his average by 5?
2. What if the player had played 15 innings with the same average, how many runs would he need to score in the 16th inning to achieve a 36 average?
3. How would the situation change if the average had to increase to 40 instead of 36?
4. If the player scores fewer than 76 runs, what will his new average be?
5. What is the effect of scoring a zero in the next innings on the average?

**Tip:** When calculating averages, always remember that the total value of all elements is the product of the average and the number of elements.

Find out how many runs a cricket player must score in his next innings to raise his average from 32 to 36. This problem involves calculating averages and solving linear equations, ideal for students in Grades 6-8.

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