Question

A deal sells an article for $Rs.24$ and gains as much percent as the cost price of the article. Find the cost price of the article.

Answer 1

It is given that selling price of an article is Rs.$24$.

Let the cost price of the article be Rs.$x$.

We know that the formula for total gain is:

$Cost\times \frac{Gain}{100}=x\times \frac{x}{100}=\frac{x^2}{100}.....\left(1\right)$

It is also given that the article gains as much present as the cost price that is:

Gain$=24-x......\left(2\right)$

Equating equations 1 and 2, we have

$24-x=\frac{x^2}{100}\Rightarrow 100(24-x)=x^2\Rightarrow x^2=2400-100x\Rightarrow x^2+100x-2400=0\Rightarrow x^2-20x+120x-2400=0\Rightarrow x(x-20)+120(x-20)=0\Rightarrow (x-20)=0,(x+120)=0\Rightarrow x=20,x=-120$

Since the cost cannot be negative thus, $x=20$.

Hence, the cost of the article is RS.$20$.