Question

The selling price of an article is 6/5 of it's cost price.If cost price of the article is 720 . Then the gain per cent is​

Answer 1

$\begin{gathered}\begin{gathered}\bf \:Given - \begin{cases} &\sf{Cost \: Price \: of \: an \: article = Rs \: 720} \\ &\sf{Selling \: Price = \dfrac{6}{5}Cost \: Price } \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:To\: find - \begin{cases} &\sf{gain \: \%}  \end{cases}\end{gathered}\end{gathered}$

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

‎ ‎ ‎ ‎ ‎ ‎We're given with the selling price and the cost price of the article. And we're asked to find the gain percent on selling 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.

In this question, we're only going to deal with the first three sub-topics which are mentioned above.

Let's start calculating the required answer!

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

$\rm :\longmapsto\: \boxed{ \tt \: gain \: = \: Selling \: Price - Cost \: Price}$

$\rm :\longmapsto\: \boxed{ \tt \: gain\% = \dfrac{gain}{Cost \: Price} \times 100\%}$

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

Given that

• Cost Price of an Article = Rs 720

Now,

$\rm :\longmapsto\:Selling \: Price = \dfrac{6}{5} \times Cost \: Price$

$\rm :\longmapsto\:Selling \: Price = \dfrac{6}{5} \times 720$

$\rm :\longmapsto\:Selling \: Price = \: Rs \: 864$

So,

$\rm :\longmapsto\:gain \: = Selling \: Price - Cost \: Price$

$\rm :\longmapsto\:gain \: = \: 864 - 720$

$\rm :\longmapsto\:gain \: = \: Rs \: 144$

Now,

$\rm :\longmapsto\:gain\% = \dfrac{gain}{Cost \: Price} \times 100\%$

$\rm :\longmapsto\:gain\% = \dfrac{144}{720} \times 100\%$

$\rm :\implies\: \boxed{ \bf \: gain\% = 20\%}$

Additional Information :-

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