Math, asked by PurviMittal280708, 3 months ago

a shopkeeper sells an article and earn profit of 30 %. if he sold the article of rs 52000 cp =​

Answers

Answered by MasterDhruva
10

Given :-

Selling price of an article :- ₹52000

Profit percentage :- 30%

To Find :-

Cost price of the article

Formula required :-

{\large \tt \dashrightarrow \orange{\boxed{\tt \gray{\dfrac{100}{(100 + Profit \bf\%)} \times Selling \: price}}}}

How to do :-

Here, we are given that the cost price of an article is ₹52000 and he gained 30% by selling that article. So, we should find the cost price of an article. We can find the cost price by using the formula given above. If the shopkeeper had obtained loss then we should subtract 100 and loss percentage in the denominator in the given formula.

Solution :-

Cost price of an article :-

{\tt \longrightarrow \dfrac{100}{(100 + 30)} \times 52000}

{\tt \longrightarrow \dfrac{100}{\cancel{130}} \times \cancel{52000} = \dfrac{100}{1} \times 400}

{\tt \longrightarrow \dfrac{100 \times 400}{1} = \dfrac{40000}{1}}

{\tt \longrightarrow \cancel \dfrac{40000}{1} = \boxed{\tt Rs \: \: 40000}}

\Huge\therefore The cost price of an article is 40000.

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\dashrightarrow Some related formulas :-

Profit :- {\boxed{\tt SP-CP}}

Loss :- {\boxed{\tt CP-SP}}

Profit percentage :- {\boxed{\tt\dfrac{Profit}{CP} \times 100}}

Loss percentage :- {\boxed{\tt\dfrac{Loss}{CP} \times 100}}

Selling price :- {\boxed{\tt\dfrac{(100 + Profit \bf\%)}{100} \times CP}}

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More to know :-

  • Cost price is the amount at which an item is bought.
  • Selling price is the amount at which an item is sold.
  • Profit is obtained when the selling price is greater than the cost price.
  • Loss is obtained when the cost price is greater than the selling price.
Answered by DüllStâr
34

 \gray{ \bf \large \dag{}Required \: Solution }

 \\

Given:

  • Profit % = 30 %
  • S.P [Selling price]= ₹52000

 \\

To find:

  • C.P [Cost price]

 \\

Solution:

 \\

We know:

 \purple  \bigstar {\boxed{ \rm{}C.P. =\sf \dfrac{S.P. \times 100}{(100 + Profit\%)}}}

 \\

By using this formula we can find value of C.P

 \\

\leadsto{ \sf{}C.P. =\sf \dfrac{S.P. \times 100}{(100 + Profit\%)}}

 \\

\leadsto{ \sf{}C.P. =\sf \dfrac{52000 \times 100}{(100 + 30)}}

 \\

\leadsto{ \sf{}C.P. =\sf \dfrac{52000 \times 100}{(1 30)}}

 \\

\leadsto{ \sf{}C.P. =\sf \dfrac{52000 \times 100}{1 30}}

 \\

\leadsto{ \sf{}C.P. =\sf \dfrac{52000 \times 10\cancel0}{1 3\cancel0}}

 \\

\leadsto{ \sf{}C.P. =\sf \dfrac{52000 \times 10}{1 3}}

 \\

\leadsto{ \sf{}C.P. =\sf \dfrac{\cancel{52000} \times 10}{\cancel{1 3}}}

 \\

\leadsto{ \sf{}C.P. =\sf \dfrac{4000\times 10}{{1}}}

 \\

\leadsto{ \sf{}C.P. =\sf 4000\times 10}

 \\

\leadsto{  \underline{ \boxed{\sf{}C.P. =\sf 40000}}}

 \\

 \therefore \:   \sf\underline{cost \: price \: of \: articles = Rs \: 40000} \checkmark \\

 \\

Know More :D

⇢ Profit = S.P - C.P

⇢ Loss = C.P - S.P

⇢ C.P = S.P - Profit

⇢ C.P = S.P + Loss

⇢ S.P = C.P + Profit

⇢ S.P = C.P - Loss

⇢ Profit % = (Profit/C.P) × 100

⇢ Loss % = (Loss/C.P) × 100

⇢ S.P = [(100 + P%)÷100]×100

⇢ Profit = (P% ×C.P)÷100

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