Question

1. On selling an article for 48. a shopkeeper loses 20%. In order to gain 20%, what woulin
the selling price?

2. On selling an article at a certain price a man gains 10%. On selling the same arte
double the price, gain per cent is​

Answer 1

Answer:

1 one answer... selling price is =72

Answer 2

$\underline{\red{\mathbb{SOLUTION}}}$

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$\underline{\textbf{Some Using Formulas}}$

Relationship between C.P. , S.P. , profit\% & \loss \% is given by ......

$\boxed{\red{Profit\%=\frac{Profit \:Amount}{C.P.}\times100\%}}$

And

$\boxed{\red{loss\%=\frac{loss\:Amount}{C.P.}\times100\%}}$

where,

$\rightarrow\textbf{profit amount=S.P.-C P.}$

$\rightarrow\textbf{loss amount=C.P.-S.P.}$

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❍$\underline{\mathbb{\red{LET \:HEAD \:TO\: THE\: PROBLEM :- 1}}}$

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$Given= \begin{cases}</p><p></p><p>\text{when , Selling prize of article 48 Rs } \\</p><p></p><p> \text{ then, loss percentage is 20\% } </p><p></p><p>\end{cases}$

,NoW=

$To Find= \begin{cases}</p><p></p><p>\text{ Selling prize of article } \\</p><p></p><p> \text{ when, profit percentage is 20\% } </p><p></p><p>\end{cases}$

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let, the cost price of the article is x rupees.

❏ 1'st part of the problem

selling the article at rupees 48 he loss 20%

$\therefore$Loss Amount=(x-48)Rs

Now , Equation is ...

$\therefore 20=\frac{}{}\times100\\</p><p>\bf\Longrightarrow \frac{\cancel{20}}{\cancel{100}}=\frac{x-48}{x}\\</p><p>\bf\Longrightarrow \frac{1}{5}=\frac{x-48}{x}\\</p><p>\bf\Longrightarrow 5(x-48)=x\\</p><p>\bf\Longrightarrow5x-240=x\\</p><p>\bf\Longrightarrow 5x-x=240\\</p><p>\bf\Longrightarrow 4x=240\\</p><p>\bf\Longrightarrow x=\frac{\cancel{240}}{\cancel{4}}\\</p><p>\bf\Longrightarrow\boxed{ x=60\: Rs}</p><p>$

❏ 2'nd Part of the Problem

In order to gain 20%profit , He would sell the article at price =$\bf S.P._{20\%\: profit}$

$\therefore Profit \;Amount=(\bf S.P._{20\%\: profit}-60)\:Rs$

Now, the profit Percentage is 20%.

$\therefore 20=\frac{(\bf S.P._{20\%\: profit}-60)}{60}\times100\\</p><p></p><p>\bf\Longrightarrow \frac{\cancel{20}}{\cancel{100}}=\frac{(\bf S.P._{20\%\: profit}-60)}{60}\\</p><p>\bf\Longrightarrow \frac{1}{5}=\frac{(\bf S.P._{20\%\: profit}-60)}{60}\\</p><p>\bf\Longrightarrow 5(\bf S.P._{20\%\: profit}-60)=60\\</p><p>\bf\Longrightarrow 5(\bf S.P._{20\%\: profit})-60\times5=60\\</p><p>\bf\Longrightarrow 5(\bf S.P._{20\%\: profit})=60+300\\</p><p>\bf\Longrightarrow \bf S.P._{20\%\: profit}=\frac{360}{5}\\</p><p>\bf\Longrightarrow \bf S.P._{20\%\: profit}=\frac{\cancel{360}}{\cancel5}\\</p><p>\bf\Longrightarrow \boxed{\red{\bf S.P._{20\%\: profit}=72\:Rs}}</p><p>$

$\therefore$ Selling Price is =72 Rs

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❍$\underline{\mathbb{</strong><strong>\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>{</strong><strong>LET</strong><strong> \:HEAD \:TO\: THE\: PROBLEM :- </strong><strong>2</strong><strong>}}</strong><strong>}</strong><strong>$

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❏ 1st part of the problem

Let, the cost price of the article is =y Rs

Now, on selling the article he gained 10% profit.

$\therefore 10=\frac{S.P.-y}{y}\times100\\</p><p>\bf\Longrightarrow \frac{10}{100}=\frac{S.P.-y}{y}\\</p><p>\bf\Longrightarrow \frac{1}{10}=\frac{S.P.-y}{y}\\</p><p>\bf\Longrightarrow 10(S.P.-y)=y\\</p><p>\bf\Longrightarrow 10 S.P.-10y=y\\</p><p>\bf\Longrightarrow 10 S.P.=y+10y\\</p><p>\bf\Longrightarrow\bf\boxed{ S.P.=\frac{11y}{10}}</p><p>$

❏ 2'nd part of the problem

Now, the selling price is doubled

$\therefore \footnotesize{\bf The \:selling \:price \:is \:now=(\frac{11y}{\cancel{10}}\times\cancel{2})=\frac{11y}{5}\:Rs}$

$\therefore Profit\: Amount=(\frac{11y}{5}-y)=\frac{6y}{5}\:Rs$

therefore,

$\bf\Longrightarrow Profit\%=\frac{\frac{6y}{5}}{y}\times100\%\\</p><p>\bf\Longrightarrow Profit\%=\frac{6\cancel{y}}{\cancel5\cancel{y}}\times\cancel{100}\%\\</p><p>\bf\Longrightarrow Profit\%=(6\times20)\%\\</p><p></p><p>\bf\Longrightarrow \bf\boxed{\red{Profit\%=120\%}}$

$\therefore$The Gain Percent is =120%

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$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

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