Question

the marked price of an article is rs 2800 which is 10% above cost price . if it is sold by allowing 20% discount , what would be gain percent?​

Answer 1

Correct Question :

The marked price of an article was rs. 2,800 which was 40% above the cost price. If it was sold by allowing a 20% discount, what will be the profit percent?

AnswEr :

• Marked Price ( MP ) = Rs. 2800
• 40% above Cost Price ( CP )

• Calculation of cost price of article :

$\longrightarrow \tt CP \times (100 + 40)\%= MP \\ \\\longrightarrow \tt CP \times 140\%= 2800 \\ \\\longrightarrow \tt CP \times \dfrac{140}{100} = 2800 \\ \\ \longrightarrow \tt CP = \cancel{2800} \times \dfrac{100}{ \cancel{140}} \\ \\\longrightarrow \tt CP = 20 \times 100 \\ \\\longrightarrow \purple{\tt CP =Rs.\:2000}$

◗ Cost Price of the Article is Rs. 2000

$\rule{300}{1}$

• Marked Price ( MP ) = Rs. 2800
• Discount% = 20%

• Calculation of selling price of article :

$\longrightarrow \tt SP = MP \times (100 - Discount)\% \\ \\\longrightarrow \tt SP = MP \times (100 - 20)\%\\\\\longrightarrow \tt SP = 2800 \times 80\% \\ \\\longrightarrow \tt SP = 28 \cancel{00} \times \dfrac{80}{ \cancel{100}} \\ \\\longrightarrow \tt SP = 28 \times 80 \\ \\\longrightarrow \purple{\tt SP =Rs.\:2240}$

◗ Selling Price of the Article is Rs. 2240

$\rule{300}{2}$

$\implies \tt Gain\% = \dfrac{Gain}{CP} \times 100 \\ \\\implies \tt Gain\% = \dfrac{SP-CP}{CP} \times 100 \\ \\\implies \tt Gain\% = \dfrac{2240-2000}{20 \cancel{00}} \times \cancel{100}\\ \\\implies \tt Gain\% = \cancel\dfrac{240}{20} \\ \\\implies \boxed{ \red{ \tt Gain\% =12\%}}$

⠀

∴ Gain Percentage on Article is 12%.

$\rule{300}{3}$

$\boxed{\begin{minipage}{7 cm}\underline{\text{Some Important Formulae Related to it :}}\\ \\ SP=CP\times(100+\sf Profit)\%\\ \\SP=CP\times(100-Loss)\%\\ \\Profit\%=\dfrac{Profit}{CP}\times100 \\ \\Loss\%=\dfrac{Loss}{CP}\times100\end{minipage}}$

#answerwithquality #BAL

Answer 2

❑Correct Question

The marked price of an article is rs 2800 which is 40% above cost price . if it is sold by allowing 20% discount , what would be gain percent?

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\huge\boxed{\mathbb{\red{SOLUTION}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\mathbb{\blue{USING \:FORMULAS}}}$

The relation between C.P. , S.P. , profit% and loss %is given by

$\Longrightarrow \boxed{\red{profit\%=\frac{Profit Amount}{C.P.}\times 100\%}}\\</p><p>\bf AND\\</p><p>\Longrightarrow\boxed{ \red{loss\%=\frac{Loss Amount}{C.P.}\times 100\%}}$

Where,

•profit Amount=S.P.- C.P.

•loss amount=C.P.-S.P.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

❍$\underline{\red{\mathbb{LET'S \:SOLVE \:THE\: PROBLEM}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$Given \begin{cases}</p><p></p><p>\text{Marked price of the Article is=2800 Rs} \\</p><p></p><p> \text{M.P. is 10\% above the cost price } </p><p></p><p>\end{cases}$

$To\: find\begin{cases}</p><p></p><p>\text{if, it is sold allowing 20\% discount on M.P.} \\</p><p></p><p> \text{ Find the gain percentage=?} </p><p></p><p>\end{cases}$

Now, let the cost prize of that article is =X Rs

Now, M.P. of that article is 40% above the cost prize,

$\therefore M.P.=C.P.+40\% \:of \:C.P\\</p><p></p><p></p><p>\bf\Longrightarrow M.P.=X+40\%\times X\\</p><p></p><p>\bf\Longrightarrow M.P.=X(1+\frac{40}{100})$

$\bf\Longrightarrow M.P.=X\times(\frac{14\cancel0}{10\cancel0})\\</p><p>\bf\Longrightarrow M.P.=\frac{14X}{10}\\</p><p>\bf\Longrightarrow X=M.P.\times\frac{10}{14}</p><p>\\</p><p>\bf\Longrightarrow X=(\cancel{2800}\times\frac{10}{\cancel{14}})</p><p>\\</p><p>\bf\Longrightarrow X=200\times 10\\</p><p>\bf\Longrightarrow \boxed{\bf\red{X=2000\:Rs}}</p><p>$

$\therefore C.P.=2000\:Rs$

Now, He sold the Article by allowing 20%Discout on ,

$\therefore S.P.=M.P.-20\%\:of \:M.P.\\</p><p>\bf\Longrightarrow S.P.=M.P.(1-\frac{20}{100})\\</p><p>\bf\Longrightarrow S.P.=28\cancel{00}\times\frac{80}{1\cancel{00}}\\\\\:\:\:\:\{\green{\because M.P.=2800\:Rs\:(given)\}}\\\\</p><p>\bf\Longrightarrow\boxed{ \red{S.P.=2240 \:Rs}}</p><p>$

Now C.P.=2000 Rs

$\therefore$ProfitAmount=(2240-2000)=240 Rs

$\therefore Profit\%=\frac{profit Amount}{C.P.}\times100\%\\</p><p>\bf\Longrightarrow Profit\%=\frac{240}{20\cancel{00}}\times1\cancel{00}\%\\</p><p>\bf\Longrightarrow Profit\%=\frac{\cancel{24}\cancel0}{\cancel2\cancel0}\%\\</p><p>\bf\Longrightarrow \bf\boxed{\red{Profit\%=12\%}}\\</p><p>\huge{\red{\mathbb{OR}}}\\</p><p></p><p>\bf\Longrightarrow \bf\boxed{\red{Gained\%=12\%}}</p><p>$

$\therefore$ Gained percentage is =12%

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

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

$\mathcal{ \&#35;\mathcal{answer with quality }\: \: \&#38; \: \: \&#35;BAL }$