To find the total number of students in Prachi's class, we need to add the number of students above her in the ranking (from the top) and the number of students below her in the ranking (from the bottom), and then subtract one (to remove the double counting of Prachi herself).

Let's assume that there are 'x' students above Prachi in the ranking and 'y' students below her in the ranking.

From the information given in the question, we know that Prachi ranks 16th from the top and 15th from the bottom. Therefore, we can write two equations based on the given information:

1) x + 15 = y (Prachi is 15th from the bottom)
2) x + y + 1 = total number of students (Adding the number of students above and below Prachi, and subtracting Prachi herself)

To solve these equations, we can substitute the value of y from equation 1 into equation 2:

x + (x + 15) + 1 = total number of students
2x + 16 = total number of students

Now, let's substitute the value of x from equation 1 into this equation:

2(x + 15) + 16 = total number of students
2x + 30 + 16 = total number of students
2x + 46 = total number of students

So, the total number of students in Prachi's class is 2x + 46.

Since we need to find the value of x, let's solve equation 1:

x + 15 = y
x = y - 15

Now, substitute this value of x into the equation for the total number of students:

total number of students = 2(y - 15) + 46
total number of students = 2y - 30 + 46
total number of students = 2y + 16

We know that Prachi ranks 15th from the bottom, so y = 15. Substitute this value into the equation:

total number of students = 2(15) + 16
total number of students = 46

Therefore, there are 46 students in Prachi's class.

However, none of the given options match this answer. So, there might be some error in the question or options provided.