A cricketer has a mean score of 60 runs in 10 innings. Find out how many runs are to be scored in the eleventh innings to raise the mean score to 62?

Options

A. 80
B. 81
C. 83
D. 82

Answer

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

### Step 1: Calculate the total runs scored in the first 10 innings.
The mean score of the cricketer is given as 60 runs over 10 innings. To find the total runs scored in these innings, we use the formula:

\[ \text{Total Runs} = \text{Mean} \times \text{Number of Innings} \]

Substituting the values:

\[ \text{Total Runs} = 60 \times 10 = 600 \text{ runs} \]

### Step 2: Calculate the total runs needed for 11 innings to achieve a mean of 62.
Now, we want to find out the total runs required to achieve a mean score of 62 after 11 innings. We use the same formula:

\[ \text{Total Runs for 11 Innings} = \text{Mean} \times \text{Number of Innings} \]

Substituting the values:

\[ \text{Total Runs for 11 Innings} = 62 \times 11 = 682 \text{ runs} \]

### Step 3: Determine the runs needed in the 11th innings.
To find out how many runs the cricketer needs to score in the 11th innings to raise the average to 62, we subtract the total runs scored in the first 10 innings from the total runs needed for 11 innings:

\[ \text{Runs needed in 11th innings} = \text{Total Runs for 11 Innings} - \text{Total Runs in 10 Innings} \]

Substituting the values:

\[ \text{Runs needed in 11th innings} = 682 - 600 = 82 \text{ runs} \]

### Conclusion:
The cricketer needs to score **82 runs** in the 11th innings to raise his mean score to 62.

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