In a class of 40 students, Anjali’s rank is thrice that of Anita. There are 4 students who have ranks worse than that of Anjali. Anita’s rank in the class is:

The correct option is 12^th.

Let Anita's rank in the class be denoted by $x$.
According to the problem statement, Anjali's rank is thrice that of Anita. Therefore, Anjali's rank is:
$3x$

We are given that the total number of students in the class is 40.
It is also stated that there are 4 students who have ranks worse than that of Anjali. This means there are 4 students ranked below Anjali. In a ranking list where rank 1 is the best and rank 40 is the worst, having 4 students with ranks worse than Anjali means Anjali's rank is 4 positions away from the very last rank (40^th).
Mathematically, we can determine Anjali's rank by subtracting the number of students ranked below her from the total number of students:
Anjali's Rank = Total students - Students ranked worse than Anjali
Anjali's Rank = $40-4=36$

Now, we can set up an equation relating Anjali's rank to Anita's rank:
$3x=36$

To find Anita's rank ($x$), we divide both sides by 3:
$x=\frac{36}{3}$
$x=12$

Thus, Anita's rank in the class is 12^th.