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

Solution:

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)

$\Rightarrow \frac{100 x+x^{2}}{100}=75$

$\Rightarrow x^{2}+100 x=7500$

$\Rightarrow x^{2}+100 x-7500=0$

$\Rightarrow x^{2}+150 x-50 x-7500=0$

$\Rightarrow x(x+150)-50(x+150)=0$

$\Rightarrow(x-50)(x+150)=0$

$\Rightarrow x-50=0$ or $x+150=0$

$\Rightarrow x=50$ or $x=-150$

∴ x = 50                   (Cost price cannot be negative)

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

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