Answer : Option C

Explanation :

$MF#%\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}$MF#%