A trader allows a trade discount of 20% and a cash discount of $${\text{ 6}}\frac{1}{4}\% $$   on the marked price of the goods and gets a net gain of 20% of the cost. By how much above the cost should the goods be marked for the sale = ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Single equivalent discount }} \cr & = \left( {20 + \frac{{25}}{4} - \frac{{20 \times 25}}{{400}}} \right)\% \cr & = 25\% \cr} $$
Let cost price of article = Rs. 100
∴ Selling price of article = Rs. 120 (20% profit)
Let the marked price of article = Rs. x
$$\eqalign{ & \therefore x \times \frac{{75}}{{100}} = 120 \cr & \Rightarrow x = \frac{{120 \times 100}}{{75}} \cr & \Rightarrow x = {\text{Rs}}{\text{. 160}} \cr & {\text{Required percentage }} \cr & {\text{ = }}\frac{{160 - 100}}{{100}} \times 100 \cr & = 60\% \cr} $$