The average score of a cricketer for 13 matches is 42 runs . If his average score for the first 5 matches is 54, then what is his average score (in runs) for last 8 matches ?

Options

A. 37
B. 39
C. 34.5
D. 33.5

Explanation

To solve the problem step by step, we will break down the information given and calculate the required average score for the last 8 matches.

### Step 1: Calculate the total score for 13 matches
The average score of the cricketer for 13 matches is given as 42 runs.

To find the total score for these 13 matches, we use the formula for average:
\[ \text{Total Score} = \text{Average} \times \text{Number of Matches} \]
Thus,
\[ \text{Total Score for 13 matches} = 42 \times 13 = 546 \]

### Step 2: Calculate the total score for the first 5 matches
The average score for the first 5 matches is given as 54 runs.

Using the same formula:
\[ \text{Total Score for 5 matches} = 54 \times 5 = 270 \]

### Step 3: Calculate the total score for the last 8 matches
To find the total score for the last 8 matches, we subtract the total score of the first 5 matches from the total score of all 13 matches:
\[ \text{Total Score for last 8 matches} = \text{Total Score for 13 matches} - \text{Total Score for 5 matches} \]
Substituting the values we calculated:
\[ \text{Total Score for last 8 matches} = 546 - 270 = 276 \]

### Step 4: Calculate the average score for the last 8 matches
Now, to find the average score for the last 8 matches, we use the average formula again:
\[ \text{Average Score for last 8 matches} = \frac{\text{Total Score for last 8 matches}}{\text{Number of Matches}} \]
Thus,
\[ \text{Average Score for last 8 matches} = \frac{276}{8} = 34.5 \]

### Final Answer
The average score for the last 8 matches is **34.5 runs**.

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