The correct answer is (a).
Let $x$ be the batsman’s average after 16 innings. Then his total score after 16 innings is $16x$. In his 17th inning, he scores 85, so his total score after 17 innings is $16x+85$. His average after 17 innings is therefore $\frac{16x+85}{17}$. We are told that this average is 2 runs higher than his average after 16 innings, so we have the equation $\frac{16x+85}{17}=x+2$. Solving for $x$, we get $x=37$. Therefore, his average after 17 innings is $\frac{16x+85}{17}=\boxed{37}$.
Option (b) is incorrect because it is the average after 16 innings, not after 17 innings. Option (c) is incorrect because it is 2 runs lower than the average after 16 innings, not 2 runs higher. Option (d) is incorrect because it is 4 runs lower than the average after 16 innings.