A dealer sells an article for ₹ $\displaystyle 75$ and gains as much percent as the cost price of the article. Find the cost price of the article.

(a)

/DA2AB/$\displaystyle 21$

Let the cost price of the article be ₹ x ∴ Gain \(\displaystyle \%=\mathrm{x}\) \[\begin{aligned} & \Rightarrow \mathrm{x}=\frac{75-\mathrm{x}}{\mathrm{x}} \times 100 \\ & \Rightarrow \mathrm{x}^{2}+100 \mathrm{x}-7500=0 \\ & \Rightarrow(\mathrm{x}-50)(\mathrm{x}+150)=0 \\ & \mathrm{x} \neq-150 \therefore \mathrm{x}=50 \end{aligned} \] So, the cost price of the article is ₹ $\displaystyle 50$