The average weight of students in a class is calculated as 45 kg. However, it was later discovered that one student's weight was incorrectly recorded as 84 kg instead of the correct value of 48 kg. This calculation error caused the reported average weight of the class to increase by 0.9 kg. Determine the total number of students in the class.

The correct option is 40.

Given Data:
- Calculated average weight of the class = 45 kg
- Incorrectly recorded weight of the student = 84 kg
- Correct weight of the student = 48 kg
- Increase in the reported average weight = 0.9 kg

Let $N$ represent the total number of students in the class.

Step 1: Find the error in the total sum of weights.

The extra weight added to the class sum due to the recording mistake is:

$\text{Total weight error}=84-48=36\text{kg}$

Step 2: Relate the total error to the change in average.

The increase in reported average weight is equal to the total weight error divided by the total number of students:

$\text{Increase in average}=\frac{\text{Total weight error}}{N}$

Substitute the known values into the formula:

$0.9=\frac{36}{N}$

Step 3: Solve for the total number of students ($N$).

Rearranging the equation to solve for $N$:

$N=\frac{36}{0.9}$

$N=\frac{360}{9}$

$N=40$

Therefore, the total number of students in the class is 40.