A batsman makes a score of 81 runs in the 16th match and thus increases his average by 3. What is his average after the 16th match

Options

A. 35
B. 34
C. 33
D. 36

Answer

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

### Step 1: Define the Variables
Let the average score of the batsman after the first 15 matches be \( x \).

### Step 2: Calculate Total Runs Before the 16th Match
The total runs scored in the first 15 matches can be expressed as:
\[ \text{Total runs in 15 matches} = 15x \]

### Step 3: Add the Score of the 16th Match
The batsman scores 81 runs in the 16th match. Therefore, the total runs after 16 matches will be:
\[ \text{Total runs in 16 matches} = 15x + 81 \]

### Step 4: Calculate the New Average After 16 Matches
The new average after the 16th match will be:
\[ \text{New average} = \frac{15x + 81}{16} \]

### Step 5: Set Up the Equation for Average Increase
According to the problem, the new average is 3 runs more than the previous average:
\[ \frac{15x + 81}{16} = x + 3 \]

### Step 6: Clear the Fraction
To eliminate the fraction, multiply both sides of the equation by 16:
\[ 15x + 81 = 16(x + 3) \]

### Step 7: Expand the Right Side
Expanding the right side gives:
\[ 15x + 81 = 16x + 48 \]

### Step 8: Rearrange the Equation
Rearranging the equation to isolate \( x \):
\[ 15x - 16x = 48 - 81 \]
\[ -x = -33 \]

### Step 9: Solve for \( x \)
Multiplying both sides by -1 gives:
\[ x = 33 \]

### Step 10: Calculate the New Average
Now that we have the average after the first 15 matches, we can find the average after the 16th match:
\[ \text{New average} = x + 3 = 33 + 3 = 36 \]

### Final Answer
The average after the 16th match is **36**.

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