A dealer 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.

Given:

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

To do:

We have to find the cost price of the article.

Solution:

Selling price of the article$=Rs. 24$.

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

This implies,

Gain % $=x$% 

We know that,

$Gain %= \frac{SP-CP}{CP}\times100$%

Therefore,

$x=\frac{24-x}{x}\times100$

$x(x)=100(24-x)

$x^2=2400-100x$

$x^2+100x-2400=0$

Solving for $x$ by factorization method, we get,

$x^2+120x-20x-2400=0$

$x(x+120)-20(x+120)=0$

$(x+120)(x-20)=0$

$x+120=0$ or $x-20=0$

$x=-120$ or $x=20$

Therefore, the value of $x$ is $20$.   ($x$ cannot be negative)

The cost price of the article is $Rs. 20$.

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Updated on: 10-Oct-2022

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