Question

A discount of 15% is given on the marked price of an article which is sold for Rs-2975. If the marked price is 40% above the cost price, calculate the profit in Rs. made by the sale of the article?​

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Answer 1

Given :

• Discount % = 15 %
• Selling Price = Rs.2975
• Profit % = 40 %

To Find :

• Profit = ?

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\dag$ Formula Used :

$\qquad \; {\orange{\bigstar \; \; {\red{\underbrace{\underline{\purple{\sf{ S.P = \bigg\{ \dfrac{100 - Discount \; \% }{100} \bigg\} \times M.P }}}}}}}}$

$\qquad \; {\orange{\bigstar \; \; {\red{\underbrace{\underline{\purple{\sf{ C.P = \bigg\{ \dfrac{100}{100 + Profit \; \% } \bigg\} \times M.P }}}}}}}}$

Where :

• S.P = Selling Price
• M.P = Marked Price
• C.P = Cost Price

$\dag$ Calculating the Marked Price :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { S.P = \bigg\{ \dfrac{100 - Discount \; \% }{100} \bigg\} \times M.P } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 2975 = \bigg\{ \dfrac{100 - 15 }{100} \bigg\} \times M.P } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 2975 = \bigg\{ \dfrac{85}{100} \bigg\} \times M.P } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 2975 = \bigg\{ \dfrac{85}{100} \bigg\} \times M.P } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 2975 \times 100 = 85 \times M.P } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 297500 = 85 \times M.P } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \dfrac{297500}{85} = M.P } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \cancel\dfrac{297500}{85} = M.P } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\pmb{\underline{\boxed{\pink{\sf{ Marked \; Price = Rs. \; 3500 }}}}}} \\ \\ \\ \\ \end{gathered}$

$\dag$ Calculating the Cost Price :

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { C.P = \bigg\{ \dfrac{100}{100 + Profit \; \% } \bigg\} \times M.P } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { C.P = \bigg\{ \dfrac{100}{100 + 40 } \bigg\} \times 3500 } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { C.P = \bigg\{ \dfrac{100}{140} \bigg\} \times 3500 } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { C.P = \dfrac{350000}{140} } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { C.P = \cancel\dfrac{350000}{140} } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; {\pmb{\underline{\boxed{\purple{\sf{ Cost \; Price = Rs. \; 2500 }}}}}} \\ \\ \\ \\ \end{gathered}$

$\dag$ Calculating the Profit :

${\twoheadrightarrow{\qquad{\sf{ Profit = Selling \; Price - Cost \; Price }}}} \\ \\ \\ \\ \ {\twoheadrightarrow{\qquad{\sf{ Profit = 2975 - 2500 }}}} \\ \\ \\ \\ \ {\twoheadrightarrow \; {\pmb{\underline{\boxed{\red{\sf{ Profit = Rs. \; 475 }}}}}}}$

$\therefore \;$ The Shop gained a profit of Rs.475 .

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Answer 2

Step-by-step explanation:

The Shop gained a profit of Rs.475 .