Question

A Lady sells an article at a gain of 5%. if she had sold it at $63 less,she would have lost 2%. find the out the cost price of the article?

Answer 1

❏ Solution :-

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✏ Given :

• Sold the article at a gain of 5 % .
• if she sold it $63 less , she would have lost 2% .

✏ To Find :

• Cost price of the article = ?

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Let , the Cost price of the article is = $X

$\footnotesize{\underline{\red{case:1}}}$

Solding the article he gained 5% ,

∴ $profit\:\%=\footnotesize{\dfrac{\text{selling prize-cost prize}}{cost\:prize}\times100\%}$

➩ $5=\footnotesize{\dfrac{\text{selling prize-X}}{X}\times100\%}$

➩ $5\%=\footnotesize{\dfrac{\text{selling prize-X}}{X}\times100\%}$

➩ $\dfrac{\cancel5}{\cancel{100}}=\footnotesize{\dfrac{\text{selling prize-X}}{X}}$

➩ $\dfrac{1}{20}=\footnotesize{\dfrac{\text{selling prize-X}}{X}}$

➩ $X=20\footnotesize{(selling \:prize-X)}$

➩ $X=20\footnotesize{(selling\: prize)-20X}$

➩ $X+20X=20\footnotesize{(selling \:prize)}$

➩ $21X=20\footnotesize{(selling \:prize)}$

➩ $\boxed{selling \:prize=\dfrac{21}{20}X}$

$\footnotesize{\underline{\red{case:2}}}$

if she sold it $63 less , she would have lost 2% .

✏ New selling prize = $(Selling price - 63)

✏ New selling prize = $ $\Bigg(\dfrac{21}{20}X-63\Bigg)$

✏ New selling prize = $ $\Bigg(\dfrac{21X-1260}{20}\Bigg)$

∴ $loss\:\%=\footnotesize{\dfrac{\text{cost prize-New selling prize }}{cost\:prize}\times100\%}$

➩ $2\%=\footnotesize{\dfrac{X-\dfrac{21X-1260}{20}}{X}}\times100\%$

➩ $\dfrac{\cancel2}{\cancel{100}}=\footnotesize{\dfrac{\dfrac{20X-21X+1260}{20}}{X}}$

➩ $\dfrac{1}{50}=\footnotesize{\dfrac{(-X+1260)}{20X}}$

➩ $\footnotesize{20X=50(-X+1260)}$

➩ $\footnotesize{ 20X=-50X+1260\times50}$

➩ $\footnotesize{ 20X+50X=1260\times50}$

➩ $\footnotesize{70X=1260\times50}$

➩ $\footnotesize{X=\dfrac{1260\times50}{70}}$

➩ $\footnotesize{X=\dfrac{\cancel{1260}\times50}{\cancel{70}}}$

➩ $\footnotesize{X=18\times50}$

➩ $\red{\large{ \boxed{X=\ 900}}}$

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∴ The cost price of the article is = $900