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