Question

if a boy sells a book for rs 450, he makes a loss of 10%. To gain 10%, what should be the selling price ?​

Answer 1

Step-by-step explanation:

AnswEr :

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

Given

SP=Rs.450

Loss%=10%

CP=?

• Calculation of Cost Price of the Book :

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

⟶SP=CP×(100−Loss)%

⟶450=CP×(100−10)%

⟶450=CP×90%

⟶450=CP×

100

90

⟶

450

×

90

100

=CP

⟶5×100=CP

⟶CP=Rs.500

$\rule{300}{1}$

• Calculation of New Selling Price :

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

NewData

CP=Rs.500

Profit%=10%

SP=?

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

⟹SP=CP×(100+Profit)%

⟹SP=500×(100+10)%

⟹SP=500×110%

⟹SP=5

00

×

1

00

110

⟹SP=5×110

⟹

SP=Rs.550

⠀

∴ To Gain 10% SP Should be Rs. 550

\rule{300}{2}[/tex]

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

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