A batman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his average after 17th match

Options

A. 36
B. 37
C. 38
D. 39

Answer

To solve the problem step by step, we will denote the average score of the batsman after 16 matches as \( x \).

### Step 1: Define the average before the 17th match
Let the average score after 16 matches be \( x \).

### Step 2: Calculate the total runs scored in the first 16 matches
Since the average score is \( x \), the total runs scored in the first 16 matches can be calculated as:
\[ \text{Total runs after 16 matches} = 16 \times x \]

### Step 3: Add the score from the 17th match
In the 17th match, the batsman scores 87 runs. Therefore, the total runs after 17 matches will be:
\[ \text{Total runs after 17 matches} = 16x + 87 \]

### Step 4: Calculate the new average after 17 matches
After the 17th match, the average increases by 3, making the new average:
\[ \text{New average} = x + 3 \]

### Step 5: Set up the equation for the new average
The new average can also be expressed as the total runs divided by the number of matches (which is 17):
\[ \frac{16x + 87}{17} = x + 3 \]

### Step 6: Multiply both sides by 17 to eliminate the fraction
\[ 16x + 87 = 17(x + 3) \]

### Step 7: Expand the right side
\[ 16x + 87 = 17x + 51 \]

### Step 8: Rearrange the equation to isolate \( x \)
Subtract \( 16x \) from both sides:
\[ 87 = 17x - 16x + 51 \]
This simplifies to:
\[ 87 = x + 51 \]

### Step 9: Solve for \( x \)
Subtract 51 from both sides:
\[ x = 87 - 51 \]
\[ x = 36 \]

### Step 10: Calculate the new average after the 17th match
Now that we have \( x \), we can find the new average:
\[ \text{New average} = x + 3 = 36 + 3 = 39 \]

### Final Answer
The average after the 17th match is **39**.

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