Question

a shopkeeper loses 20% on selling an article for rs1000. what should be the selling price if he wants to make a profit of 20%?

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Answer 1

Answer:

1440 rupees

Step-by-step explanation:

Answer 2

Given:

Original loss % = 20%

Original Selling Price (S.P.) of the article = ₹1,000

New profit % = 20%

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To find:

New Selling price of the article to earn a profit of 20%.

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Solution:

We are given that,

Original loss % = 20%

Original S.P. = ₹1,000

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Hence we can find the Cost Price (C.P.) of the article, which is given by the formula:

$\boxed {\sf {\red {C.P. = \dfrac {S.P. \times 100}{100-L \%}}}}$

On substituting the values in the formula,

$\implies \sf {C.P. = \dfrac {1000 \times 100}{100-20}}$

$\implies \sf {C.P. = \dfrac {1,00,000}{80}}$

$\implies {\sf {\pink {C.P. = Rs.\ 1,250}}}$

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Now,

C.P. = ₹1,250

New profit % = 20%

New S.P. = ?

We can find the new S.P. of the article, which is given by the formula:

$\boxed {\sf {\red {S.P. = \dfrac {100+P \%}{100} \times C.P.}}}$

On substituting the values in the formula,

$\implies \sf {S.P. = \dfrac {100+20}{100} \times 1,250}$

$\implies \sf {S.P. = \dfrac {120}{100} \times 1,250}$

$\implies \sf {S.P. = \dfrac {12}{10} \times 1,250}$

$\implies \sf {S.P. = 12 \times 125}$

$\boxed {\bf {\green {S.P. = Rs.\ 1,500}}}$

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Final answer:

Hence, the man should sell the article for ₹1,500 in order to gain a profit of 20%.