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
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