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
Step-by-step explanation:
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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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