Question

A shopkeeper sells an article at loss of 12.5%. Had he sold it for Rs. 51.80 more then he would have earned a profit of 6%. The cost price of the article is: *​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• A shopkeeper sells an article at loss of 12.5%.

Let assume that

Cost Price of an article = Rs x

Loss % = 12.5 %

We know,

$\boxed{ \rm{ \:Selling \: Price = \dfrac{(100 - loss\%) \times Cost \: Price}{100} \: }}$

So, on substituting the values, we get

$\rm \: Selling \: Price = \dfrac{(100 - 12.5) \times x}{100}$

$\rm\implies \:\rm \: Selling \: Price = \dfrac{87.5x}{100}$

Now, further given that had he sold it for Rs. 51.80 more then he would have earned a profit of 6%.

Now,

$\rm \: Cost \: Price \: = \: Rs \: x$

$\rm \: Selling \: Price \: = \: Rs \: \dfrac{87.5x}{100} + 51.80$

$\rm \: Profit \:\% \: = \: 6 \: \%$

We know,

$\boxed{ \rm{ \:Selling \: Price = \dfrac{(100 + Profit\%) \times Cost \: Price}{100} \: }}$

$\rm \: \dfrac{87.5x}{100} + 51.80 = \dfrac{(100 + 6) \times x}{100}$

$\rm \: \dfrac{87.5x + 5180}{100} = \dfrac{106x}{100}$

$\rm \: 87.5x + 5180 = 106x$

$\rm \: 5180 = 106x - 87.5x$

$\rm \: 18.5x = 5180$

$\rm\implies \:x = 280$

Thus,

$\rm\implies \:\boxed{ \rm{ \:Cost \: Price \: of \: an \: article \: = \: Rs \: 280 \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) or(100-Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$