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.

Step-by-Step Explanation:

To find the total number of students in the class, we analyze how the recording error affected the total weight and the overall average weight of the class.

Step 1: Calculate the extra weight recorded due to the error
One student's weight was incorrectly recorded as 84 kg instead of the actual weight of 48 kg. The difference between the wrong weight and the correct weight represents the excess weight added to the total calculation.

$\text{Excess weight recorded}=84-48=36\text{kg}$

Step 2: Relate total weight error to the average weight increase
The change in average weight is determined by distributing the total excess weight equally among all students in the class.

$\text{Increase in average weight}=\frac{\text{Excess weight}}{\text{Total number of students (N)}}$

Step 3: Set up the equation and solve for N
We are given that the calculation error caused the reported average weight of the class to increase by 0.9 kg. Substituting the values into our formula:

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

Rearranging the equation to solve for N:

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

$N=40$

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