Question

OOU 8. An article is marked 50% above the cost price and it is sold at a discount of 40%. What is the gain or loss percentage ? © (A) 10% loss (B) 15% gain (C) 15% loss (D) 10% gain ଗୋଟିଏ ଦ୍ରବ୍ୟର ଲିଖିତ ମୂଲ୍ୟ ଏହାର କ୍ରୟ ମୂଲ୍ୟଠାରୁ ଶତକତା 50 ଅଧୁକ ଏବଂ ଏହାକୁ ଶତକଡା 40 ରିହାତି ଦିଆଯାଇ ବିକ୍ରି କରାଗଲା । ତେବେ ଶତକତା କେତେ ଲାଭ ବା କ୍ଷତି ହେବ ? (A) 10% କ୍ଷତି (B) 15% ଲାଭ (C) 15% କ୍ଷତି (D) 10% ଲାଭ 9. Fill in the missing nu​

Answer 1

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

Given that,

• An article is marked 50% above the cost price.

Let assume that

• Cost Price of an Article = Rs 100

So,

$\rm \: Marked \: Price = Cost \: Price + 50\% \: of \: Cost \: Price$

$\rm \: = \: 100 + \dfrac{50}{100} \times 100$

$\rm \: = \: 100 + 50$

$\rm \: = \: 150$

$\red{\rm\implies \:\boxed{ \rm{ \:Marked \: Price \: = \: Rs \: 150 \: \: }}}$

Now, We have

$\rm \: Marked \: Price \: = \: Rs \: 150$

$\rm \: Discount \: \% \: = \: 15 \: \%$

Now, we know that

$\rm \: Selling \: Price = \dfrac{(100 - Discount\%) \times Cost \: Price}{100}$

So, on substituting the values, we get

$\rm \: = \: \dfrac{(100 - 40) \times 150}{100}$

$\rm \: = \: \dfrac{60\times 15}{10}$

$\rm \: = \: \dfrac{6\times 15}{1}$

$\rm \: = \: 90$

$\red{\rm\implies \:\boxed{ \rm{ \:Selling \: Price \: = \: Rs \: 90 \: \: }}}$

Now, we have

$\rm \: Cost \: Price \: = \: Rs \: 100$

$\rm \: Selling \: Price \: = \: Rs \: 90$

$\rm\implies \:Cost \: Price \: > \: Selling \: Price$

$\rm\implies \:There \: is \: loss \: in \: this \: transaction.$

So,

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

$\rm \: Loss\% = \frac{100 - 90}{100} \times 100 \: \%$

$\red{\rm\implies \:\boxed{ \rm{ \:Loss \: \% \: = \: 10 \: \% \: \: }}}$

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

Additional Information :-

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