The average weight of the students of a class is 45 kg. If the weight of a student calculated mistakenly as 84 kg instead of 48 kg, due to which the average weight of the students increased by 0.9, then find the total no. of students in the class.

The correct option is 40.

Step-by-Step Explanation:

1. Understand the difference in weight:

The weight of one student was mistakenly recorded as 84 kg instead of the actual weight of 48 kg.

Error in total weight = Mistaken weight - Actual weight

$\text{Error in total weight}=84-48=36\text{kg}$

2. Understand the effect on the average:

Due to this extra 36 kg counted in the total weight, the average weight of the class increased by 0.9 kg.

The formula relating the total change in sum, the number of students, and the change in average is:

$\text{Total Increase in Weight}=\text{Number of Students}\times \text{Increase in Average Weight}$

3. Calculate the number of students:

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

$36=N\times 0.9$

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

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

$N=40$

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