To solve this question, let's break it down step by step:

Step 1: Understand the problem
The problem states that a batsman in his 17th innings scores 85 runs and increases his average by 3. We need to find the batsman's average after 17 innings.

Step 2: Define the variables
Let's define the initial average of the batsman as A. The number of innings played before the 17th innings is 16.

Step 3: Calculate the total runs before the 17th innings
The total runs scored before the 17th innings can be calculated by multiplying the average (A) by the number of innings (16). So the total runs before the 17th innings would be 16A.

Step 4: Calculate the new average
To calculate the new average, we need to consider the runs scored in the 17th innings. The total runs after the 17th innings would be the total runs before the 17th innings plus the runs scored in the 17th innings (85). The number of innings played after the 17th innings would be 17.

So the new average can be calculated as (16A + 85) / 17.

Step 5: Set up the equation
According to the problem, the new average is 3 more than the initial average. So we can set up the equation as:

(16A + 85) / 17 = A + 3

Step 6: Solve the equation
Let's solve the equation to find the value of A:

16A + 85 = 17(A + 3)
16A + 85 = 17A + 51
85 - 51 = 17A - 16A
34 = A

So the initial average (A) is 34.

Step 7: Calculate the new average
Now that we have found the initial average, we can calculate the new average after 17 innings using the equation:

New average = (16A + 85) / 17
New average = (16 * 34 + 85) / 17
New average = (544 + 85) / 17
New average = 629 / 17
New average = 37

Therefore, the batsman's average after 17 innings is 37. Option B is the correct answer.