Question

By selling an article for Rs 960 a man incurs a loss of 4% . what is the cost price of the article ?​

Answer 1

$\begin{gathered}\begin{gathered}\bf \:Given - \begin{cases} &\sf{Selling \: Price \: of \: an \: article \: = \: Rs \: 960} \\ &\sf{Loss\% \: = \: 4 \: \%} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:To\:find - \:\begin{cases} &\sf{Cost \: Price \: of \: an \: article}  \end{cases}\end{gathered}\end{gathered}$

$\large \underline{\tt \:{Understanding \: the \: concept: }}$

‎ ‎ ‎ ‎ ‎ ‎We're given with the selling price and the Loss percent by selling an article. And we're asked to find the cost price of the article.

For finding this, first let's recall the chapter- "Profit and Loss", which we've studied in previous classes!

• Cost Price (C.P.) - The price at which an article is purchased is called it's cost price.

• Selling Price (S.P.) - The price at which an article is sold is called it's selling price.

• Profit - If the S.P. of an article is greater than its C.P., we say that there is a profit.

• Loss - If the S.P. of an article is less than its C.P., we say that there is a loss.

• Overheads - All the expenditure incurred on transportation, repairs, etc are categorised as overheads. Overheads are always included in the C.P. of the article.

Let's start calculating the required answer!

$\begin{gathered}\Large{\bold{{\underline{Formula\:Used - }}}} \end{gathered}$

$\rm :\longmapsto\: \large\boxed{ \tt \: Cost \: Price = \dfrac{100 \times Selling \: Price}{100 - Loss \: \% \: } }$

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

Given that

• Selling Price of an Article = Rs 960

• Loss % = 4 %

Now,

• Cost Price of an Article is evaluated as

$\rm :\longmapsto\:Cost \: Price = \dfrac{Selling \: Price \times 100}{100 - Loss\%}$

$\rm :\longmapsto\:Cost \: Price = \dfrac{960 \times 100}{100 - 4}$

$\rm :\longmapsto\:Cost \: Price = \dfrac{96000}{96}$

$\rm :\longmapsto\: \boxed{ \bf \: Cost \: Price \: = \: Rs \: 1000}$

Additional Information :-

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