Question

By reducing the selling price of an article by $Rs.50,$ a gain of $5\%$ turns into a loss of $5\%.$ Find the original selling price of the article.

Answer 1

Let the Original selling price be $x$

With profit i.e. Gain of $5\%$, the selling price is $(x+5\%$ of $x)=(x+0.05x)=1.05x$
With loss i.e. Loss of $5\%$, the selling price is $(x-5\%$ of $x)=(x-0.05x)=0.95x$

given that, there will be a difference in $S.P$ when sold at $5\%$ profit and when sold at a loss of $5\%,$ and that difference is $Rs.50.$

$\therefore 1.05x-0.95x=50$
$\Rightarrow 0.10x=50$
$\Rightarrow x=500$
Hence, the Original selling price is $Rs.500.$