A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half $$\frac{1}{2}$$ . The number of pupils in the class is:

$$\eqalign{ & {\text{Let}}\,{\text{there}}\,{\text{be}}\,x\,{\text{pupils}}\,{\text{in}}\,{\text{the}}\,{\text{class}}{\text{.}} \cr & {\text{Total}}\,{\text{increase}}\,{\text{in}}\,{\text{marks}} \cr & = {x \times \frac{1}{2}} = \frac{x}{2} \cr & \therefore \frac{x}{2} = \left( {83 - 63} \right) \cr & \Rightarrow \frac{x}{2} = 20 \cr & \Rightarrow x = 40 \cr} $$