# A shopkeeper give 1 article free of every purchase of 15 article and also gives a discount of 4 % and after all that his profit percent is 35%. Find CP:MP.

Let the mark price of one article =MP=10 x
The shopkeeper sells a total of 16 articles.
$\Rightarrow$ The mark price of 16 articles =160 x
Given:
The shopkeeper gives 1 article free on the purchase of 15 articles.
$\Rightarrow$ The selling price of 16 articles = The mark price of 15 articles =150 x

Now, a further discount of 4% is given,
$\Rightarrow$ The final selling price of 16 articles =150 x [(100-4) / 100]=144 x
The shopkeeper earns a profit of 35 \%
$\Rightarrow$ The cost price of 16 article =144 x [100 /(100+35)]=320 x / 3
$\Rightarrow$The cost price of 1 article =CP=320 x / 48=20 x / 3

So $\frac{CP}{MP}=\frac{\frac{20x}{3}}{10x}=\frac{2}{3}$

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