#### കുറിപ്പുകൾ (Short Notes)

Answer : Option C

Explanation :

\begin{align} &\text{Let CP = x} \\ \\ &\text{Percentage profit earned by selling an item for Rs. 1920} \\ \\ &= \dfrac{SP-CP}{CP} \times 100 \\ \\ &= \dfrac{1920-x}{x} \times 100 \\ \\ \\ &\text{Percentage loss incurred by selling the same item for Rs. 1280}\\ \\ &= \dfrac{CP-SP}{CP} \times 100 \\ \\ &= \dfrac{x-1280}{x} \times 100 \\ \\ \\ &\text{Given that Percentage profit earned by selling an item for Rs. 1920} = \\ &\text{Percentage loss incurred by selling the same item for Rs. 1280} \\ \\ &\Rightarrow \dfrac{1920-x}{x} \times 100 = \dfrac{x-1280}{x} \times 100\\ \\ &\Rightarrow \dfrac{1920-x}{x} = \dfrac{x-1280}{x} \\ \\ &\Rightarrow 1920 – x = x – 1280 \\ \\ &\Rightarrow 2x = 1920 + 1280 = 3200 \\ \\ &\Rightarrow x = \dfrac{3200}{2} \\ \\ &= 1600 \\ \\ \\ &\text{Required Selling Price} = CP \times \dfrac{125}{100} \\ \\ &= 1600 \times \dfrac{125}{100} = 1600 \times \dfrac{5}{4} \\ \\ &= 400 \times 5 = 2000 \end{align} 