Math, asked by nilamsingh5790, 6 days ago

|8. A merchant allows 25% discount on the marked price of the cycles and still makes a profit of 20/% If he gains 360 over the sale of one cycle, find the marked price of the cycle. Cycle.​

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Answered by mathdude500
20

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

Given that,

A merchant allows 25% discount on the marked price of the cycles and still makes a profit of 20/% If he gains 360 over the sale of one cycle.

Let assume that Marked Price of cycle be x.

Discount % = 25 %

We know,

\boxed{ \rm{ \:Selling \: Price =  \frac{(100  - Discount\%)\times Marked \: Price}{100} \: }} \\

So, on substituting the values, we get

\rm \: Selling \: Price = \dfrac{(100 - 25) \times x}{100}

\rm \: Selling \: Price = \dfrac{75 \times x}{100}

\rm\implies \:Selling \: Price \:  =  \: \dfrac{3x}{4}  \\

Now, It is further given that after allowing 25% discount on the marked price of the cycles, he still makes a profit of 20 %

So, we know

\boxed{ \rm{ \:Cost \: Price =  \frac{100 \times Selling \: Price}{100 + Profit\%}  \: }}

So, on substituting the values, we get

\rm \: Cost \: Price \:  =  \: \dfrac{100}{100 + 20} \times \dfrac{3x}{4}  \\

\rm \: Cost \: Price \:  =  \: \dfrac{25}{120} \times 3x  \\

\rm \: Cost \: Price \:  =  \: \dfrac{25}{40} \times x  \\

\rm \: Cost \: Price \:  =  \: \dfrac{5x}{8}   \\

Now, Further given that, Gain on one cycle is 360

\rm \: Selling \: Price - Cost \: Price = 360 \\

\rm \: \dfrac{3x}{4}  - \dfrac{5x}{8}  = 360 \\

\rm \: \dfrac{6x - 5x}{8}   = 360 \\

\rm \: \dfrac{x}{8}   = 360 \\

\rm\implies \:x = 2880 \\

So, Marked price of cycle is 2880.

\rule{190pt}{2pt}

Additional Information :-

\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}

Answered by Anonymous
7

☯↪Refer to the attachment :⬅

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