By selling an article for ₹ $\displaystyle 48$, a trader loses as much percent as half of the cost price of the article. Calculate the cost price and loss amount of the article.

Let the cost price (CP)of the article be ₹ \(\displaystyle x\) Loss \(\displaystyle =\frac{x}{2} \%\) of \(\displaystyle x=\frac{x^{2}}{200}\) Selling price \(\displaystyle =48=x-\frac{x^{2}}{200}\) \(\displaystyle \Rightarrow x^{2}-200 x+9600=0\) \(\displaystyle \Rightarrow(x-120)(x-80)=0\) \(\displaystyle \Rightarrow x=120,80\) When \(\displaystyle \mathrm{CP}=₹ 120\), Loss \(\displaystyle =120-48=₹ 72\) When \(\displaystyle \mathrm{CP}=₹ 80\), Loss \(\displaystyle =80-48=₹ 32\)