Whatever pivot is selected quick sort worst case O(n^2)
but here it is given that this procedure takes $O(n^2)$ time and in original quick sort, it takes O(1) time because we go to that index in array and select it and then do the partition procedure. Here, I think, we have to include $O(n^2)$ in recurrence.
So, recurrence will look like $T(n) = T(74) +T(n-75) + O(n^2) + O(n)$
O(n^2) to select pivot then partition will take O(n) time and after partition, 74 elements which are right of 75th greatest elements will be more than 75th greatest element and elements on left side will be less than that 75th greatest element. Now here T(74) will be constant(c) and now we have to solve recurrence to find running time.
please correct me if I am wrong.