A batsman has a certain average of runs for 16 innings.In the 17th inning, he makes a score of 85 runs there by increasing the average by 3. what is the average of 17 innings?

Options

A. 38
B. 37
C. 36
D. 35

Answer

To solve the problem step by step, let's denote the average runs scored by the batsman in the first 16 innings as \( x \).

### Step 1: Calculate the total runs for the first 16 innings
The total runs scored in the first 16 innings can be expressed as:
\[ \text{Total runs for 16 innings} = 16x \]

### Step 2: Calculate the total runs after 17 innings
In the 17th inning, the batsman scores 85 runs. Therefore, the total runs after 17 innings will be:
\[ \text{Total runs for 17 innings} = 16x + 85 \]

### Step 3: Calculate the new average after 17 innings
The average after 17 innings is given by the total runs divided by the number of innings:
\[ \text{Average after 17 innings} = \frac{16x + 85}{17} \]

### Step 4: Set up the equation based on the increase in average
According to the problem, this new average is 3 runs more than the previous average \( x \):
\[ \frac{16x + 85}{17} = x + 3 \]

### Step 5: Solve the equation
To eliminate the fraction, multiply both sides by 17:
\[ 16x + 85 = 17(x + 3) \]
Expanding the right side:
\[ 16x + 85 = 17x + 51 \]

### Step 6: Rearranging the equation
Now, rearranging the equation to isolate \( x \):
\[ 16x + 85 - 51 = 17x \]
\[ 34 = 17x - 16x \]
\[ 34 = x \]

### Step 7: Calculate the average for 17 innings
Now that we have \( x \), which is the average for the first 16 innings, we can find the average for the 17 innings:
\[ \text{Average for 17 innings} = x + 3 = 34 + 3 = 37 \]

### Final Answer
The average of the batsman for 17 innings is:
\[ \boxed{37} \]