Let Anjali's rank be \(A\) and Anita's rank be \(N\).
Anjali's rank is three times Anita's rank, so \(A = 3N\).
There are 4 students with ranks worse than Anjali's. This indicates Anjali's rank is \(40 - 4 = 36\).
Thus, \(A = 36\).
Substituting \(A = 36\) into \(A = 3N\), we get \(36 = 3N\), leading to \(N = \frac{36}{3} = 12\).
Consequently, Anita's rank is 12th.