Question
How much percent above the cost price should a shopkeeper mark his goods so as to earn a profit of 32% after allowing a discount of 12% on the marked price ?
Answer: Option A
$$\eqalign{
& \Rightarrow \frac{{{\text{Cost price}}}}{{{\text{Marked price}}}} \cr
& {\text{ = }}\frac{{100 - {\text{Discount}}\% }}{{100 + {\text{Profit}}\% }} \cr
& {\text{ = }}\frac{{100 - 12}}{{100 + 32}} \cr
& {\text{ = }}\left. {\frac{{88}}{{132}}} \right]{\text{ 44}} \cr
& \therefore {\text{Required }}\% {\text{ }} \cr
& = \frac{{44}}{{88}} \times 100 \cr
& = 50\% \cr} $$
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$$\eqalign{
& \Rightarrow \frac{{{\text{Cost price}}}}{{{\text{Marked price}}}} \cr
& {\text{ = }}\frac{{100 - {\text{Discount}}\% }}{{100 + {\text{Profit}}\% }} \cr
& {\text{ = }}\frac{{100 - 12}}{{100 + 32}} \cr
& {\text{ = }}\left. {\frac{{88}}{{132}}} \right]{\text{ 44}} \cr
& \therefore {\text{Required }}\% {\text{ }} \cr
& = \frac{{44}}{{88}} \times 100 \cr
& = 50\% \cr} $$
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