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 ?

Options

A. 76
B. 70
C. 4
D. 2

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the total runs scored in the first 10 innings.
The average runs scored by the player in 10 innings is given as 32.

To find the total runs scored in these innings, we use the formula for average:
\[ \text{Total Runs} = \text{Average} \times \text{Number of Innings} \]
So,
\[ \text{Total Runs} = 32 \times 10 = 320 \]

### Step 2: Determine the new average after the next innings.
The player wants to increase his average by 4 runs. Therefore, the new average will be:
\[ \text{New Average} = 32 + 4 = 36 \]

### Step 3: Calculate the total runs needed for 11 innings to achieve the new average.
Now, we need to find out the total runs that would give him this new average over 11 innings:
\[ \text{Total Runs for 11 Innings} = \text{New Average} \times \text{Number of Innings} \]
So,
\[ \text{Total Runs for 11 Innings} = 36 \times 11 = 396 \]

### Step 4: Find out how many runs he needs to score in the next innings.
To find out how many runs he needs to score in his next innings, we subtract the total runs scored in the first 10 innings from the total runs needed for 11 innings:
\[ \text{Runs Needed in Next Innings} = \text{Total Runs for 11 Innings} - \text{Total Runs for 10 Innings} \]
So,
\[ \text{Runs Needed in Next Innings} = 396 - 320 = 76 \]

### Conclusion:
The player must score **76 runs** in his next innings to increase his average by 4 runs.

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