Question

a shopkeeper marks the price of the article in such a way that after allowing 28% discount he wants a gain of 12% if the marked price is rs224 the the cost price of the article is??​

Answer 1

Solution :

Given Marked Price of Article is Rs 224 and Discount = 28%

Let's Find Discount Amount First :

$\sf \star \: \: 28\% \: of \: 224$

$\hookrightarrow \sf \cancel \dfrac{6272}{100}$

$\hookrightarrow \sf Rs \: 62.72$

Let's Find Selling Price Now

$\bigstar \boxed{ \sf \: Selling \: Price = Marked \: Price - \: Discount }$

$\hookrightarrow \sf \: Rs \:( 224 - 62.72)$

$\hookrightarrow \sf \: Rs \: 161.28$

Given Profit % = 12%

Let's Find Cost Price Now

$\bigstar \boxed{ \sf \: Cost \: Price = \frac{Selling \: Price \times 100}{100 + Profit }}$

$\hookrightarrow \sf \dfrac{161.28 \times 100}{100 + 12}$

$\hookrightarrow \sf \cancel \dfrac{16128}{112}$

$\hookrightarrow \sf \: Rs \: 144$

Hence,Cost Price of the Article is Rs 144

Answer 2

AnswEr :

Rs.144.

$\bf{\purple{\underline{\underline{\bf{Given\::}}}}}$

A shopkeeper marks the price of the article in such a way that after allowing 28% discount he wants a gain of 12% .If the marked price is Rs.224.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The price of the article (Cost price) .

$\bf{\orange{\underline{\underline{\bf{Explanation\::}}}}}$

$\bf{We\:have}\begin{cases}\sf{Discount,(D)=28\%}\\ \sf{Profit\%=12\%}\\ \sf{Marked\:price,(M.P.)=Rs.224}\end{cases}}$

Formula use :

$\bf{\boxed{\bf{Discount=\frac{Marked\:price\times Discount\%}{100} }}}}}}$

A/q

$\Rightarrow\tt{Discount=\dfrac{224\times 28}{100} }\\\\\\\\\Rightarrow\tt{Discount=\cancel{\dfrac{6272}{100} }}\\\\\\\\\Rightarrow\tt{\pink{Discount=Rs.62.72}}$

So,

$\leadsto\sf{Selling\:price,(S.P.)=Marked\:price-Discount}\\\\\\\leadsto\sf{Selling\:price,(S.P.)=Rs.(224-62.72)}\\\\\\\leadsto\sf{\red{Selling\:price,(S.P.)=Rs.161.28}}$

A shopkeeper gain of 12%, we get;

Formula use :

$\bf{\boxed{\bf{Cost\:price,(C.P.)=\frac{100}{100+profit\%} \times S.P.}}}}}}}$

$\mapsto\tt{C.P.=\dfrac{100}{100+12} \times 161.28}\\\\\\\\\mapsto\tt{C.P.=\dfrac{100}{112} \times 161.28}\\\\\\\\\mapsto\tt{C.P.=\cancel{\dfrac{16128}{112} }}\\\\\\\\\mapsto\tt{\red{C.P.=Rs.144}}$

Thus,

$\bf{\large{\underbrace{\sf{The\:cost\:of\:the\:article\:is\:\:Rs.144}}}}}}}$