Question

A dealer sells a toy for $₹24$ and gains as much percent as the cost price of the toy. Find the cost price of the toy.

Answer 1

Given selling price, $\mathrm{SP}=₹24$

Dealer gains as much percent as the cost price of the article.

Let cost price be $₹x$

So, $\mathrm{Gain}\%=\mathrm{x}$

We know that,

$\begin{array}{rcl}\mathrm{Gain}\%& =& \frac{(\mathrm{SP}–\mathrm{CP})\times 100}{\mathrm{CP}}\\ \mathrm{x}& =& \frac{(24-\mathrm{x})\times 100}{\mathrm{x}}\\ {\mathrm{x}}^2+100\mathrm{x}-2400& =& 0\\ {\mathrm{x}}^2+120\mathrm{x}-20\mathrm{x}-2400& =& 0\\ \mathrm{x}(\mathrm{x}+120)-20(\mathrm{x}+120)& =& 0\\ (\mathrm{x}+120)(\mathrm{x}-20)& =& 0\\ & \Rightarrow & \mathrm{x}=-120\mathrm{or}\mathrm{x}=20\end{array}$

We neglect $\mathrm{x}=-120$ since the cost price cannot be negative.

$\mathrm{So}\mathrm{x}=20$

Hence the cost price of the toy is $₹20$.