In a class with a certain number of students, if one student weighting 50 kg is added n average weight of class increased by 1 kg. If one more student weighting 50 kg is added, n average weight of class increased by 1.5 kg over original average. What is original average weight (in kg) of class?

Let the original average weight of the class be x kg and let there be n students.
Then, sum of weights of n students = (nx) kg
$$\eqalign{ & \therefore \frac{{nx + 50}}{{n + 1}} = x + 1 \cr & \Rightarrow nx + 50 = \left( {n + 1} \right)\left( {x + 1} \right) \cr & \Rightarrow nx + 50 = nx + x + n + 1 \cr & \Rightarrow x + n = 49 \cr & \Rightarrow 2x + 2n = 98.....(i) \cr & {\text{And,}} \cr & \Rightarrow \frac{{nx + 100}}{{n + 2}} = x + 1.5 \cr & \Rightarrow nx + 100 = \left( {n + 2} \right)\left( {x + 1.5} \right) \cr & \Rightarrow nx + 100 = nx + 1.5n + 2x + 3 \cr & \Rightarrow 2x + 1.5n = 97.....(ii) \cr} $$
Subtracting (ii) from (i), we get: 0.5n = 1 or n = 2
Putting n = 2 in (i), we get: x = 47