Let the cost price of the article be $x$

$\therefore$ Gain percent $=x \%$

According to the given condition,

$\Rightarrow \frac{100 x+x^{2}}{100}=75$
$\Rightarrow x^{2}+100 x=7500$
$\Rightarrow x^{2}+100 x-7500=0$
$\Rightarrow x^{2}+150 x-50 x-7500=0$
$\Rightarrow x(x+150)-50(x+150)=0$
$\Rightarrow(x-50)(x+150)=0$
$\Rightarrow x-50=0$ or $x+150=0$
$\Rightarrow x=50$ or $x=-150$
$\therefore x=50 \quad$ (Cost price cannot be negative)

Hence, the cost price of the article is 50 .