Question

by selling an article for Rs 368 among a man loss 8% what prices should be sold to gain 10%​

Answer 1

$\red{A}\pink{N}\orange{S}\green{W}\blue{E}\gray{R}$

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.

Answer 2

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

Given that,

$\rm \: Selling \: Price \: of \: an \: article \: = \: Rs \: 368$

$\rm \: Loss \: \% \: = \: 8 \: \% \:$

We know, Selling Price, Cost Price and Loss % are connected by the relationship,

$\boxed{ \rm{ \:Cost \: Price \: = \: \frac{100 \times Selling \: Price}{100 - Loss\%} \: }}$

So, on substituting the values, we get

$\rm \: Cost \: Price \: = \: \dfrac{100 \times 368}{100 - 8}$

$\rm \: Cost \: Price \: = \: \dfrac{100 \times 368}{92}$

$\rm \: Cost \: Price \: = \: 100 \times 4$

$\rm\implies \:Cost \: Price \: = \: Rs \: 400$

Now, we have

$\rm \: Cost \: Price \: of \: an \: article \: = \: Rs \: 400$

$\rm \: Gain\% \: = \: 10 \: \%$

We know, Selling Price, Cost Price and Gain % are connected by the relationship,

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

So, on substituting the values, we get

$\rm \: Selling \: Price = \dfrac{(100 + 10) \times 400}{100}$

$\rm \: Selling \: Price = 110 \times 4$

$\rm\implies \:\boxed{ \rm{ \:Selling \: Price \: = \: Rs \: 440 \: \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

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