Average of 10 matches is 32, How many runs one should should score to increase his average by 4 runs.

Options

A. 70
B. 76
C. 78
D. 80

Answer

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

### Step 1: Calculate the total runs scored in the first 10 matches.
The average of the 10 matches is given as 32. To find the total runs scored in these matches, we can use the formula:

\[ \text{Total Runs} = \text{Average} \times \text{Number of Matches} \]

Substituting the values:

\[ \text{Total Runs} = 32 \times 10 = 320 \]

### Step 2: Determine the new average after the next match.
The problem states that we want to increase the 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 matches to achieve the new average.
Now that we know the new average, we can calculate the total runs required for 11 matches:

\[ \text{Total Runs for 11 Matches} = \text{New Average} \times \text{Number of Matches} \]

Substituting the values:

\[ \text{Total Runs for 11 Matches} = 36 \times 11 = 396 \]

### Step 4: Calculate the runs needed in the next match.
To find out how many runs need to be scored in the next match, we subtract the total runs scored in the first 10 matches from the total runs required for 11 matches:

\[ \text{Runs Needed in Next Match} = \text{Total Runs for 11 Matches} - \text{Total Runs in 10 Matches} \]

Substituting the values:

\[ \text{Runs Needed in Next Match} = 396 - 320 = 76 \]

### Final Answer:
The number of runs one should score in the next match to increase his average by 4 runs is **76**.

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