An article is sold at a profit of 20% . If the cost price is increased by 10% and the sale price by Rs. 26, then the percentage of profit reduces by 5% . Determine the cost price = ?

Solution(By Examveda Team)

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