The averages of runs scored by a cricket player In 11 innings is 63 and the average of his first six innings Is 60 and the average of last six Innings is 65. Find the runs scored by him in the sixth Innings.

Options

A. 60
B. 54
C. 67
D. 57

Answer

To solve the problem, we need to find the runs scored by the cricket player in the sixth inning based on the given averages. Let's break it down step by step.

### Step 1: Calculate the total runs scored in 11 innings
The average runs scored in 11 innings is given as 63. To find the total runs scored, we can use the formula:

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

Substituting the values:

\[ \text{Total Runs} = 63 \times 11 = 693 \]

### Step 2: Calculate the total runs scored in the first 6 innings
The average runs scored in the first 6 innings is given as 60. Using the same formula:

\[ \text{Total Runs in First 6 Innings} = 60 \times 6 = 360 \]

### Step 3: Calculate the total runs scored in the last 6 innings
The average runs scored in the last 6 innings is given as 65. Again, using the formula:

\[ \text{Total Runs in Last 6 Innings} = 65 \times 6 = 390 \]

### Step 4: Set up the equation to find the runs scored in the sixth inning
Let \( x \) be the runs scored in the sixth inning. The total runs in the last 6 innings includes the runs scored in the sixth inning and the runs scored in the innings 7, 8, 9, 10, and 11.

The total runs in the last 6 innings can be expressed as:

\[ \text{Total Runs in Last 6 Innings} = \text{Runs in 6th Inning} + \text{Runs in 7th, 8th, 9th, 10th, and 11th Innings} \]

From the previous calculations, we know:

\[ 390 = x + (360 - x) \]

### Step 5: Solve for \( x \)
Now, we can simplify the equation:

\[ 390 = x + 360 - x \]

This simplifies to:

\[ 390 = 360 + x \]

Subtracting 360 from both sides gives:

\[ x = 390 - 360 = 30 \]

### Step 6: Calculate the runs scored in the sixth inning
The runs scored in the sixth inning is:

\[ x = 30 \]

### Conclusion
The runs scored by the cricket player in the sixth inning is **30**.

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