A shopkeeper marks the price of an item keeping 20% profit. If he offers a discount of $${\text{12}}\frac{1}{2}\% $$   on the marked price, his gain percent will be = ?

Let cost price of item = Rs. 100
Marked price of item = 120% of 100
$$\eqalign{ & {\text{ = }}\frac{{120}}{{100}} \times {\text{100 }} \cr & {\text{ = Rs}}{\text{. 120 }} \cr} $$
After discount, selling price = 87.5% of 120
$$\eqalign{ & \frac{{87.5}}{{100}} \times {\text{120 = Rs}}{\text{. 105}} \cr & {\text{Profit}}\% {\text{ }} = \frac{{105 - 100}}{{100}}{\text{ }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{ }}5\% {\text{ }} \cr} $$