Question

A person purchased two articles at the same price and on
selling the first article he makes a profit of 12%
Selling price of Second article is Rs 90 more than the selling price of
the first article. Find the cost price of one
article if his a overall profit percentage is 15% ​

Answer 1

$i )Let \: cost \: price \: first \: article (c.p) = Rs\:x$

$profit (g) = 12\%$

$selling \: price \: of \: first \:article (s.p _{1}) \\= c.p\Big ( \frac{100+g}{100}\Big)$

$= x \Big( \frac{ 100+12}{100} \Big) \\= \frac{112x}{100}$

$\implies s.p _{1} = 1.12x \: --(1)$

$ii) cost \: price \: second \: article (c.p) = Rs\:x$

$Selling \: price \: of \: second \: article (s.p_{2})\\= s.p _{1} + 90 \\= ( 1.12x + 90 ) \: --(2)$

$iii ) Total \: cost \: price\\ = x + x \\= Rs \: 2x$

$Total \: selling \: price\\ = s.p _{1} + s.p _{2}\\= 1.12x + ( 1.12x + 90 ) \\= 2.24x + 90$

$Total \: profit = 15\%$

$Total \: selling \: price = T.C.P\Big( \frac{100+15}{100}\Big)$

$\implies 2.24x + 90 = 2x\Big( \frac{115}{100}\Big)$

$\implies 2.24x + 90 = 2x\times 1.15$

$\implies 2.24x + 90 = 2.3x$

$\implies 90 = 2.3x - 2.24x$

$\implies 90 = 0.06x$

$\implies 90 = \frac{6}{100}x$

$\implies x = \frac{90\times 100}{6}$

$\implies x = Rs \:1500$

Therefore.,

$\red { Cost \:price \: of \: one \: article } \\\green { = Rs \:1500}$

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