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

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 \(\displaystyle =80-48=₹ 32\)