Question

By reducing the selling price of an article by $Rs50$, a gain of $5\%$ turns into a loss of $5\%$. Find the original selling price of the article?

Answer 1

Let Rs $x$ be the cost price and Rs$y$ be the the selling price of the

article.

we know that

$Gain\%=\left(\frac{Gain\times 100}{C.P}\right)$

$\therefore 5\%=\left(y-x\right)\times \frac{100}{x}$

$\Rightarrow x=20\left(y-x\right)$

$\Rightarrow x=20y-20x$

$\Rightarrow x+20x=20y$

$\Rightarrow 21x=20y$

$\Rightarrow y=\frac{21x}{20}$

When the selling price of the article is reduce by Rs$50$ then the

new selling price of article $=Rs\left(\frac{21x}{20}-50\right)$

we know that

$Loss\%=\left(\frac{loss\times 100}{C.P}\right)$

$5=\left[\frac{x-\left\{\frac{21x}{20}-50\right\}}{x}\right]\times 100$

$\Rightarrow x=\left\{\frac{x-21x}{20}+50\right\}\times 20$

$\Rightarrow x=\left[\frac{\left\{20x-21x+1000\right\}}{20}\right]\times 20$

$\Rightarrow x=-x+1000$

$\Rightarrow x+x=1000$

$\Rightarrow 2x=1000$

So, the cost price of article is Rs$500$

The original selling price $y=\frac{21x}{20}$

$=\frac{21\times 500}{20}$

$y=525$

The original selling price is Rs $525$