The weight of a person was entered incorrectly as 83 kg instead of 63 kg. As a result, the average weight of a group of people increased by 500 gm. What is the total number of people in the group?

Let, number of peoples in group = x
Average = n
⇒ nx - 63 + 83 = n(x + 500 gm)
⇒ nx + 20 = nx + $$\frac{{\text{n}}}{2}$$ kg
⇒ n = 20 × 2
⇒ n = 40

OR
$$\eqalign{ & {\text{Average}} = \frac{{{\text{Sum}}}}{{{\text{Number}}}} \cr & 500\,{\text{gm}} = \frac{{20}}{n} \cr & \frac{1}{2} = \frac{{20}}{n} \cr & n = 40 \cr} $$