Question

A dealer sells a calculator at a loss of 12% . If he had sold it at a profit of 12% he would have gained Rs.288 more . Find the cost price​

Answer 1

Question-

A dealer sells a calculator at a loss of 12% . If he had sold it at a profit of 12% he would have gained Rs.288 more . Find the cost price.

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Required Answer

• Rs.1200

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

~Used Abbreviations

• C.P=Cost price
• S.P=Selling Price

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Given-

• Loss in calculator-12 percent
• Profit=12 percent
• Rupees gained=288

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

To Find-

• Cost Price=?

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Formula Using-

$~{\large{\underline{\frak{Cost\:Price}}}}$

$\bigstar{\underline{\boxed{\red{\sf{\dfrac{100 \times rupees\:Gained}{difference\:between\:S.P\:and\:C.P}}}}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\qquad{\qquad{\quad{\Large{\underline{\underline{\blue{\sf{Solution}}}}}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

$~{\large{\underline{\frak{Calculating\:Selling\:price\:for\:profit}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{S.P_{(for\:profit)}=100+Profit\:percentage}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{S.P_{(for\:profit)}=100+12}}}}$

${\blue{\rightsquigarrow}{\qquad{\underline{\red{\sf{S.P\:for\:profit=112}}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

$~{\large{\underline{\frak{Calculating\:Selling\:price\:for\:loss}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{S.P_{(for\:loss)}=100-loss}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{S.P_{(for\:loss)}=100-12}}}}$

${\blue{\rightsquigarrow}{\qquad{\underline{\red{\sf{S.P\:for\:loss=88}}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

${\large{\underline{\frak{Calculating\:percentage\:of\:CP}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{S.P\:of\:profit-S.P\:of\:loss}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{112-88}}}}$

${\blue{\rightsquigarrow}{\qquad{\underline{\red{\sf{24\:percentage}}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

${\large{\underline{\frak{Calculating\:CP}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{C.P=\dfrac{100 \times rupees\:Gained}{difference\:between\:S.P\:and\:C.P}}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{\dfrac{C.P=100 \times 288}{24}}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{C.P=\dfrac{2800}{24}}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{C.P=\cancel\dfrac{2800}{24}}}}}$

${\blue{\rightsquigarrow}{\qquad{\underline{\red{\sf{C.P=Rs.1200}}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

~Therefore

• Cost price of calculator is=Rs.1200

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$