Question

A dealer sells an article for ₹75 and gains as much percent as the cost price of the article. Find the cost price of the article.
[CBSE 2011]

Answer 1

Let the cost price of the article be ₹x.

∴ Gain percent = x%

According to the given condition,
₹x + ₹$\left(\frac{x}{100}\times x\right)$ = ₹75 (Cost price + Gain = Selling price)
$$\begin{gathered} \Rightarrow \frac{100x+x^2}{100}=75 \\ \Rightarrow x^2+100x=7500 \\ \Rightarrow x^2+100x-7500=0 \\ \Rightarrow x^2+150x-50x-7500=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow x\left(x+150\right)-50\left(x+150\right)=0 \\ \Rightarrow \left(x-50\right)\left(x+150\right)=0 \\ \Rightarrow x-50=0\mathrm{or}x+150=0 \\ \Rightarrow x=50\mathrm{or}x=-150 \end{gathered}$$
∴ x = 50 (Cost price cannot be negative)

Hence, the cost price of the article is ₹50.