Question

By selling an article for Rs. $18.75$, a dealer loses as much per cent as its cost price. Find the cost price of the article.

Answer 1

Let the cost price be Rs. $x$
Selling price $=$ Rs. $18.75$
Loss$=$ Cost price $-$ Selling price
$\Rightarrow \frac{x}{100}\times x=x-18.75$
$\Rightarrow \frac{x^2}{100}=x-18.75$
$\Rightarrow x^2=100x-1875$
$\Rightarrow$ $x^2-100x+1875=0$
$\Rightarrow (x-75)(x-25)=0$
$\Rightarrow$ $x=75$ or $x=25$
Therefore, the cost price is Rs. $75$ or Rs. $25$.