Question

to use the trade man allows a discount of 25% on the MP how much about the CP must he mark his articles to make a profit of 17%

Answer 1

Question :-

The trade man allows a discount of 25% on the MP. How much above the CP must he mark his articles, to make a profit of 17% ?

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

Let assume that the Cost Price of Article be Rs 100

and

Marked Price of the articles be Rs x

Case :- 1

Cost Price of an article = Rs 100

Profit % = 17 %

So, Selling Price of an Article is given by

$\boxed{\sf{ \: Selling \: Price \: = \: \frac{(100 + Profit\%) \times Cost \: Price}{100} \: }}$

So, on substituting the values, we get

$\rm \: Selling \: Price \: = \: \dfrac{(100 + 17) \times 100}{100}$

$\rm\implies \:Selling \: Price \: = \: 117$

Case :- 2

Marked Price of an Article = Rs x

Selling Price of an Article = Rs 117

Discount % = 25 %

We know, Marked Price of an Article is given by

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

So, on substituting the values, we get

$\rm \: Marked \: Price \: = \: \dfrac{117 \times 100}{100 - 25}$

$\rm \: Marked \: Price \: = \: \dfrac{117 \times 100}{75}$

$\rm \: Marked \: Price \: = \: \dfrac{117 \times 4}{3}$

$\rm \: Marked \: Price \: = \: 39 \times 4$

$\rm\implies \:Marked \: Price \: = \: 156$

It means, Trade man marked his Article 56 % above the Cost Price, to earn a profit of 17 %, after allowing the discount of 25 %.

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