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# 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.

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Solution

## 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,$\begin{array}{rcl}\mathrm{Gain}%& =& \frac{\left(\mathrm{SP}–\mathrm{CP}\right)×100}{\mathrm{CP}}\\ \mathrm{x}& =& \frac{\left(24-\mathrm{x}\right)×100}{\mathrm{x}}\\ {\mathrm{x}}^{2}+100\mathrm{x}-2400& =& 0\\ {\mathrm{x}}^{2}+120\mathrm{x}-20\mathrm{x}-2400& =& 0\\ \mathrm{x}\left(\mathrm{x}+120\right)-20\left(\mathrm{x}+120\right)& =& 0\\ \left(\mathrm{x}+120\right)\left(\mathrm{x}-20\right)& =& 0\\ & ⇒& \mathrm{x}=-120\mathrm{or}\mathrm{x}=20\end{array}$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 $₹20$.  Suggest Corrections  79      Similar questions
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