Math, asked by hetsmetha7, 10 months ago

an article is sold at a gain of 16% had it been sold for rupees 200 more than gain would have been 20% find the cost price of an article​

Answers

Answered by mddilshad11ab
33

Step-by-step explanation:

let \:  \\ cp \: of \: article = x \\ a \: gain \: of \: 16\% \\ so \\ sp \: of \: article =  \frac{100 + gain\%}{100}  \times cp \\  =  \frac{100 + 16}{100}  \times x \\  =  \frac{116}{100}  \times x \\  =  \frac{29}{25} x \:  \\ if \: the \: article \: has \: been \: sold \: 200 \: more \\ than \: sp \: of \: article =  \frac{29}{25}x + 200 \\ now \\ cp \: ofarticle \:  = x \\ a \: gain \: of \: 20\% \\ so \: sp \: of \: article \:  \\  =  \frac{120}{100}  \times x \\  =  \frac{6}{5} x \\ now \:  \\ cp \: of \: article \\  =  >  \frac{6}{5} x =  \frac{29}{25} x + 200 \\  =  >  \frac{6}{5} x -  \frac{29}{25} x = 200 \\  =  >  \frac{30x - 29x}{25}  = 200 \\  =  > x = 5000 \\  \\ hence \: cp \: of \: article \: is \: 5000

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Answered by MeenakshiSen
1

Step-by-step explanation:

Step-by-step explanation:

\begin{gathered}let \: \\ cp \: of \: article = x \\ a \: gain \: of \: 16\% \\ so \\ sp \: of \: article = \frac{100 + gain\%}{100} \times cp \\ = \frac{100 + 16}{100} \times x \\ = \frac{116}{100} \times x \\ = \frac{29}{25} x \: \\ if \: the \: article \: has \: been \: sold \: 200 \: more \\ than \: sp \: of \: article = \frac{29}{25}x + 200 \\ now \\ cp \: ofarticle \: = x \\ a \: gain \: of \: 20\% \\ so \: sp \: of \: article \: \\ = \frac{120}{100} \times x \\ = \frac{6}{5} x \\ now \: \\ cp \: of \: article \\ = > \frac{6}{5} x = \frac{29}{25} x + 200 \\ = > \frac{6}{5} x - \frac{29}{25} x = 200 \\ = > \frac{30x - 29x}{25} = 200 \\ = > x = 5000 \\ \\ hence \: cp \: of \: article \: is \: 5000\end{gathered}

let

cpofarticle=x

againof16%

so

spofarticle=

100

100+gain%

×cp

=

100

100+16

×x

=

100

116

×x

=

25

29

x

ifthearticlehasbeensold200more

thanspofarticle=

25

29

x+200

now

cpofarticle=x

againof20%

sospofarticle

=

100

120

×x

=

5

6

x

now

cpofarticle

=>

5

6

x=

25

29

x+200

=>

5

6

x−

25

29

x=200

=>

25

30x−29x

=200

=>x=5000

hencecpofarticleis5000

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