by selling an article for Rs 368 among a man loss 8% what prices should be sold to gain 10%
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by selling an article for Rs 368 among a man loss 8% what prices should be sold to gain 10%
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Selling price of article =Rs.368
Let the cost price of article be Rs.x.
Now, according to the question,
x−8% of x=368
x−8/100×x=368
x-2x/25=368
25x-2x/25=368
23x/25=368
x=368×25/23=400
Therefore the cost price of article is Rs.400.
Let the new selling price of article to gain 10% be Rs.y.
Now to gain 10%,
y=400+10% of 400
⇒y=400+10/100×400
⇒y=400+40=440
Hence to gain 10%, the article mut be sold for Rs.440.
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
[tex]\rm \: Selling \: Price \: of \: an \: article \: = \: Rs \: 368 \\ [/tex]
[tex]\rm \: Loss \: \% \: = \: 8 \: \% \: \\ [/tex]
We know, Selling Price, Cost Price and Loss % are connected by the relationship,
[tex]\boxed{ \rm{ \:Cost \: Price \: = \: \frac{100 \times Selling \: Price}{100 - Loss\%} \: }} \\ [/tex]
So, on substituting the values, we get
[tex]\rm \: Cost \: Price \: = \: \dfrac{100 \times 368}{100 - 8} \\ [/tex]
[tex]\rm \: Cost \: Price \: = \: \dfrac{100 \times 368}{92} \\ [/tex]
[tex]\rm \: Cost \: Price \: = \: 100 \times 4\\ [/tex]
[tex]\rm\implies \:Cost \: Price \: = \: Rs \: 400 \\ [/tex]
Now, we have
[tex]\rm \: Cost \: Price \: of \: an \: article \: = \: Rs \: 400 \\ [/tex]
[tex]\rm \: Gain\% \: = \: 10 \: \% \\ [/tex]
We know, Selling Price, Cost Price and Gain % are connected by the relationship,
[tex]\boxed{ \rm{ \:Selling \: Price = \frac{(100 + Gain\%) \times Cost \: Price}{100} \: }} \\ [/tex]
So, on substituting the values, we get
[tex]\rm \: Selling \: Price = \dfrac{(100 + 10) \times 400}{100} \\ [/tex]
[tex]\rm \: Selling \: Price = 110 \times 4 \\ [/tex]
[tex]\rm\implies \:\boxed{ \rm{ \:Selling \: Price \: = \: Rs \: 440 \: \: }} \\ [/tex]
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Additional Information :-
[tex]\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}[/tex]