A player has a certain average for 15 innings. In the `16^(th)` inning he scores 120, thereby his average increases by 6 runs. What is the new average?

Options

A. 8
B. 30
C. 20
D. 24

Answer

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

### Step 1: Let the original average be \( x \).
The player has played 15 innings with an average of \( x \).

### Step 2: Calculate the total runs scored in the first 15 innings.
The total runs scored in the first 15 innings can be calculated as:
\[ \text{Total runs in 15 innings} = 15x \]

### Step 3: Add the score of the 16th inning.
In the 16th inning, the player scores 120 runs. Therefore, the total runs after 16 innings will be:
\[ \text{Total runs in 16 innings} = 15x + 120 \]

### Step 4: Calculate the new average after 16 innings.
The new average after 16 innings is given by:
\[ \text{New average} = \frac{15x + 120}{16} \]

### Step 5: Set up the equation based on the increase in average.
According to the problem, the new average increases by 6 runs compared to the original average. Therefore, we can set up the equation:
\[ \frac{15x + 120}{16} = x + 6 \]

### Step 6: Solve the equation.
To eliminate the fraction, multiply both sides by 16:
\[ 15x + 120 = 16(x + 6) \]
Expanding the right side:
\[ 15x + 120 = 16x + 96 \]
Now, rearranging the equation:
\[ 120 - 96 = 16x - 15x \]
\[ 24 = x \]

### Step 7: Calculate the new average.
Now that we have the original average \( x \), we can find the new average:
\[ \text{New average} = x + 6 = 24 + 6 = 30 \]

### Final Answer:
The new average is **30**.

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