Question

If a boy sells a book for RS. 450 he gets a loss 10℅ then find cost price to gain 10℅ what should be the selling price​. ​

Answer 1

AnswEr :

$\bf{ Given}\begin{cases}\sf{SP=Rs. \:450}\\\sf{Loss\%=10\%}\\ \sf{CP=?}\end{cases}$

• Calculation of Cost Price of the Book :

$\longrightarrow \tt SP = CP \times (100 - Loss)\% \\ \\\longrightarrow \tt 450 = CP \times (100 - 10)\% \\ \\\longrightarrow \tt 450 = CP \times 90\% \\ \\\longrightarrow \tt450 = CP \times \dfrac{90}{100} \\ \\\longrightarrow \tt \cancel{450} \times \dfrac{100}{\cancel{90}} = CP \\\\\longrightarrow \tt5 \times 100 = CP \\ \\\longrightarrow \pink{\tt CP = Rs. \:500}$

$\rule{300}{1}$

• Calculation of New Selling Price :

$\bf{New \:Data}\begin{cases}\sf{CP=Rs.\:500}\\\sf{Profit\%=10\%}\\ \sf{SP=?}\end{cases}$

$\Longrightarrow \tt SP = CP \times (100 + Profit)\% \\ \\\Longrightarrow \tt SP = 500 \times (100 + 10)\% \\ \\\Longrightarrow \tt SP = 500 \times 110\% \\ \\\Longrightarrow \tt SP = 5\cancel{00} \times\dfrac{110}{1\cancel{00}} \\ \\\Longrightarrow \tt SP= 5\times110 \\\\\Longrightarrow\boxed{\red{\tt SP = Rs. \:550}}$

⠀

∴ To Gain 10% SP Should be Rs. 550

$\rule{300}{2}$

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

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Answer 2

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{\boxed { \huge \mathcal\red{ solution}}}}$

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$\underline{\mathbb{USING\: FORMULA}}$

the relation between the C.P , S.P and loss percentage or profit percentage is given by...

$\implies \boxed{Profit \%=\frac{\bf Profit\:Amount}{Cost \:Prize }\times100\%}$

and

$\implies \boxed{Loss\%=\frac{\bf Loss\:Amount}{Cost \:Prize }\times100\%}$

where,

profit amount=S.P.-C.P.

loss amount=C.P.-S.P.

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$\underline{\mathbb{LET\: SOLVE \:THE \:PROBLEM}}$

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$Given = \begin{cases}</p><p></p><p>\text{Selling prize of the book is=450 Rs} \\</p><p></p><p> \text{loss percentage after selling the book is=10\%} </p><p></p><p>\end{cases}$

$To\:Find = \begin{cases}</p><p></p><p>\text{Find\: the\: selling \:price} \\</p><p></p><p>\text{To \:gain\:10\%\: profit} </p><p></p><p>\end{cases}$

Let, the cost prize of the book is=x Rs

❏First Part of the Problem:-

Now ,after selling it a price of 450Rs

he gets a loss of 10%

$\therefore$The Loss amount is=(x-450)Rs

$\therefore Loss\%=10=\frac{x-450}{x}\times100\\ \Longrightarrow \frac{\cancel{10}}{\cancel{100}}=\frac{x-450}{x}\\ \Longrightarrow \frac{1}{10}=\frac{x-450}{x}\\ </p><p>\Longrightarrow x=10(x-450)\\</p><p>\Longrightarrow x=10x-4500\\</p><p>\Longrightarrow 10x-x=4500\\</p><p>\Longrightarrow 9x=4500\\</p><p>\Longrightarrow x\frac{\cancel{4500}}{\cancel9}\\</p><p>\Longrightarrow \boxed{\bf\red{x=500\: Rs}}$

$\therefore$The cost price of the book was =500 Rs

❏ Second part of the problem:-

Now ,the Selling price at which the book should be sold to get a profit percentage of 10% is related to the equation given below,

$\Longrightarrow 10=\frac{S.P._{10\%\:profit}-500}{500}\times100\\</p><p>\Longrightarrow \frac{10}{100}=\frac{S.P._{10\%\:profit}-500}{500}\\</p><p>\Longrightarrow \frac{1}{10}=\frac{S.P._{10\%\:profit}-500}{500}\\</p><p>\Longrightarrow 500=10(S.P._{10\%\:profit}-500)\\</p><p>\Longrightarrow 500=10(S.P._{10\%\:profit})-5000\\</p><p>\Longrightarrow 10(S.P._{10\%\:profit})=500+5000\\</p><p>\Longrightarrow S.P._{10\%\:profit}=\frac{\cancel{5500}}{\cancel{10}}\\</p><p>\Longrightarrow \boxed{\red{\bf Selling\:Prize_{10\%profit}=550\:Rs} }$

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

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