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?​

Answer 1

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Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

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.

Let assume that

Marked Price of an Article is Rs x

Discount % = 15 %

Selling Price = Rs 2975

We know that,

$\boxed{\sf{  \:Marked\:Price = \dfrac{Selling \: Price \times 100}{100 - Discount\%} \: }}$

So, on substituting the values, we get

$\rm \: x = \dfrac{2975 \times 100}{100 - 15}$

$\rm \: x = \dfrac{2975 \times 100}{85}$

$\rm \: x = 35 \times 100$

$\rm\implies \:x = 3500$

$\rm\implies \:Marked\:Price \: = \: Rs \: 3500$

Now, further given that Marked price is 40 % above the cost price.

$\rm \: Marked\:Price = Cost\:Price + 40\% \: of \: Cost\:Price$

$\rm \:Cost\:Price + \dfrac{40}{100} \times Cost\:Price = 3500$

$\rm \:Cost\:Price + \dfrac{2}{5} \times Cost\:Price = 3500$

$\rm \: \dfrac{7}{5} \times Cost\:Price = 3500$

$\rm \: \dfrac{1}{5} \times Cost\:Price = 500$

$\rm\implies \:Cost\:Price \: = \: Rs \: 2500$

Now, We have

$\rm \: Cost\:Price \: = \: Rs \: 2500$

$\rm \: Selling \: Price \: = \: Rs \: 2975$

Since, Selling Price > Cost Price

So, it means there is Profit in this transaction.

Thus,

$\rm \: Profit \: = \: Selling \: Price \: - \: Cost\:Price$

$\rm \: Profit \: = \: 2975 - 2500$

$\rm\implies \:Profit \: = \: Rs \: 475$

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$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) or(100-Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$