In a class of 40 students Anuja is ranked $$17^{th}$$ and Mihir is ranked $$18^{th}$$. What will be their ranks from the last, respectively?

There are 40 students in the class and Anuja's rank is 17th from the top. 
This means there are 16 people above her and 23 below her, making her rank 24th from the bottom. 

Similarly, Mihir is 18th from the top. 
This means there are 17 people ahead hima and 22 below him, making his rank 23rd from the bottom. 

Hence, the correct answer would be 24th and 23rd. 

Therefore, Option C is the correct answer.