A showroom owner sells a leather jacket for Rs. x and claims to make a profit of 10%. He plans to have a stall in the trade fair and marks the same jacket at Rs. 2x. At the stall,he allows a discount of 20%. What will be the percentage profit that he will make at the trade fair?

Solution(By Examveda Team)

$$\eqalign{ & {\text{S}}{\text{.P}}{\text{. = Rs}}{\text{. }}x \cr & {\text{Profit = 10}}\% \cr & {\text{C}}{\text{.P}}{\text{. = Rs}}{\text{.}}\left( {\frac{{100}}{{110}} \times x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{ Rs}}{\text{.}}\frac{{10x}}{{11}} \cr & {\text{M}}{\text{.P}}{\text{. = Rs}}{\text{. }}2x, \cr & {\text{Discount = 20}}\% {\text{}} \cr} $$
S.P. at trade fair = 80% of Rs. 2x
$$\eqalign{ & {\text{ = Rs}}{\text{.}}\left( {\frac{{80}}{{100}} \times 2x} \right) \cr & = {\text{Rs}}{\text{.}}\frac{{8x}}{5} \cr & {\text{Profit = Rs}}{\text{.}}\left( {\frac{{8x}}{5} - \frac{{10x}}{{11}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{{38x}}{{55}} \cr & \therefore {\text{ Profit }}\% \cr & {\text{ = }}\left( {\frac{{38x}}{{55}} \times \frac{{11}}{{10x}} \times 100} \right)\% \cr & = 76\% \cr} $$