Practice MCQ Questions and Answer on Profit and Loss

Solution: Let the total value be Rs. x $$\eqalign{ & {\text{value of }}\frac{2}{3}{\text{rd}} = {\text{Rs}}{\text{.}}\frac{{2x}}{3} \cr & {\text{value of}}\frac{1}{3}{\text{rd}} = {\text{Rs}}.\frac{x}{3} \cr & {\text{Total S}}{\text{.P}}{\text{.}} \cr & = {\text{Rs}}.\left[ {\left( {106\% {\text{ of }}\frac{{2x}}{3}} \right) + \left( {97\% {\text{ of }}\frac{x}{3}} \right)} \right] \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{53x}}{{75}} + \frac{{97x}}{{300}}} \right) \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{309x}}{{300}}} \right) \cr & \therefore \frac{{309x}}{{300}} - x = 540 \cr & \Rightarrow \frac{{9x}}{{300}} = 540 \cr & \Rightarrow x = \left( {\frac{{540 \times 300}}{9}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 18000 \cr} $$

Solution: $$\eqalign{ & {\text{Let the C}}{\text{.P}}{\text{. be Rs}}{\text{. }}x \cr & {\text{Profit}} = 20\% \cr & {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {\frac{{120}}{{100}} \times x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{{6x}}{5} \cr & {\text{New C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{110}}{{100}} \times x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{{11x}}{{10}} \cr & {\text{New S}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {\frac{{6x}}{5} + 26} \right) \cr & {\text{New profit}} \cr & = {\text{Rs}}.\left[ {\left( {\frac{{6x}}{5} + 26} \right) - \frac{{11x}}{{10}}} \right] \cr & = {\text{Rs}}.\left( {\frac{x}{{10}} + 26} \right) \cr & \therefore \left( {\frac{x}{{10}} + 26} \right) \times \frac{{10}}{{11x}} \times 100 = 15 \cr & \Rightarrow 100\left( {x + 260} \right) = 165x \cr & \Rightarrow 65x = 26000 \cr & \Rightarrow x = 400 \cr} $$