Question

By selling an article for Rs. 900, loss of 18% occurs. At what price should the the shopkeeper sell the article to get a profit of 8%


Please answer with explanation

Answer 1

Given:-

→ Selling price (S.P.) = Rs.900

→ Loss = 18 %

→ Required profit percentage = 8 %

To find:-

→ Price at which the article should be sold

to get profit of 8 %.

Solution:-

Here, we are given with S.P. and loss %. So firstly, let's calculate the C.P. We know that :-

S.P. = C.P.(1 - Loss/100)

⇒ 900 = C.P.(1 - 18/100)

⇒ 900/C.P. = 82/100

⇒ 900/C.P. = 0.82

⇒ C.P. = 900/0.82

⇒ C.P. = Rs.1097.56

________________________________

Now :-

• C.P. = Rs.1097.56

• Profit = 8 %

• S.P.₂ = ?

S.P. = C.P.(1 + Profit/100)

⇒ S.P.₂ = 1097.56(1 + 8/100)

⇒ S.P.₂ = 1097.56(108/100)

⇒ S.P.₂ = 118536/100

⇒ S.P.₂ = Rs.1185.36

Thus, the shopkeeper should sell the article at a price of Rs.1185.36 .

Answer 2

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${\large{\bold{\rm{\underline{Let's \; understand \; the \; concept \; 1^{st}}}}}}$

★ This question says that by selling an article for Rupees 900, there is a loss occur of 18 percentage. Then the question says that we have to find out that at what price should the the shopkeeper sell the article to get a profit of 8 percentage.

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ Selling price of an article = Rs. 900

★ Loss occur on selling an article = 18%

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ At what price should the the shopkeeper sell the article to get a profit of 8 percentage.

${\large{\bold{\rm{\underline{Solution}}}}}$

★ At 1185.36 Rupees should the the shopkeeper sell the article to get a profit of 8 percentage.

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${\large{\bold{\rm{\underline{Using \; concept}}}}}$

★ Loss percentage formula(CP)

★ Profit percentage formula(SP)

${\large{\bold{\rm{\underline{Using \; formula}}}}}$

★ CP = SP × 100 / 100 - loss%

★ SP = CP(1+Profit/100)

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${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ Firstly let us find the Cost price !

↝ CP = SP × 100 / 100 - loss%

↝ CP = 900×100 / 100-18

↝ CP = CP = 90000 / 82

↝ CP = CP = 1097.56 Rupees

~ Now let's find new SP !

↝ SP = CP(1+Profit/100)

↝ SP = 1097.56(1+8/100)

↝ SP = 1097.56(108/100)

↝ SP = 1097.56(27/25)

↝ SP = 1185.36 Rupees

• † Henceforth, 1185.36 Rupees is that price on which the shopkeeper sell the article to get a profit of 8 percentage.

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${\large{\bold{\rm{\underline{Additional \; information}}}}}$

~ Sσmє mσrє knσwlєdgє rєlαtєd tσ tσpíc - Cσmpαríng Quαntítíєs

♛ Discount is a reduction given on market price.

◆ Discount = Marketed price - Sale price.

♛ Discount can be calculated when discount percentage is given.

◆ Discount = Discount percentage of Marketed Price

♛ Additional expenses made after buying an article are included in the cost price and are known to be “overhead expenses”

◆ CP = Buying Price + Overhead expenses.

♛ Sales tax is charged on sale of an item by the government and is added to the bill amount.

◆ Sale tax = Tax % of bill amount

♛ Some extra formulas -

◆ Amount when interest is compounded annually - P(1+R/100)^n

◆ Amount when interest is compounded half yearly - P(1+R/200)^2n

${\bf{Where,}}$

↝ P denotes Principal

↝ R denotes rate of interest

↝ n denotes time

↝ R/2 denotes half yearly rate

↝ 2n denotes number of half year

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Some important formulas -

$\begin{gathered}\large\boxed{ \begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Gain = S.P – C.P} \\ \\ \bigstar \:\sf{Loss = C.P – S.P} \\ \\ \bigstar \: \sf{Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{loss \: \% = \Bigg( \dfrac{loss}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{S.P = \dfrac{100+Gain\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100+Gain\%} \times S.P} \\ \\\bigstar \: \sf{ S.P = \dfrac{100-loss\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100-loss\%} \times S.P}\end{array} }\end{gathered}$

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