An article was marked at ₹ $$x$$ and sold at a discount of $$(x — 40)$$%. If the customer paid ₹ $$(x — 32)$$, then find the marked price of the article.

Given,

Marked price of the article = ₹ $$x$$

Discount% = $$(x — 40)$$%

Selling price = ₹ $$(x — 32)$$

$$=$$>  $$x-\frac{\left(x-40\right)}{100}\times x=x-32$$

$$=$$>  $$100x-\left(x-40\right)x=100x-3200$$

$$=$$>  $$-x^2+40x=-3200$$

$$=$$>  $$x^2-40x-3200=0$$

$$=$$>  $$x^2-80x+40x-3200=0$$

$$=$$>  $$x\left(x-80\right)+40\left(x-80\right)=0$$

$$=$$>  $$\left(x-80\right)\left(x+40\right)=0$$

$$=$$>  $$x-80=0$$   or   $$x+40=0$$

$$=$$>  $$x=80$$   or    $$x=-40$$

$$x$$ cannot be negative

$$=$$>  $$x=₹ 80$$

$$\therefore\ $$Marked price of the article = $$x$$ = ₹80

Hence, the correct answer is Option D