Even after a discount of x% on marked price a trader gains by y%. What is the mark up percentage over the cost price?

Let cost price of the article = P rupees. Then,

⇒ Selling price of the article = cost price + y% profit on the cost price,

⇒ Selling price of the article = $(P + P \times \frac{y}{{100}} = P\frac{{\left( {100 + y} \right)}}{{100}})$-------- (1)

Now, let the marked price of the article = Q rupees. Then,

According to the question,

⇒ Marked price – x% discount on the marked price = selling price of the article

$(\begin{array}{l} \Rightarrow \ \ \ Q - Q \times \frac{x}{{100}} = P\frac{{\left( {100 + y} \right)}}{{100}}\\ \Rightarrow\ \ \ Q\frac{{\left( {100 - x} \right)}}{{100}} = P\frac{{\left( {100 + y} \right)}}{{100}}\\ \Rightarrow \ \ \ Q = P\frac{{\left( {100 + y} \right)}}{{\left( {100 - x} \right)}} \end{array})$

Therefore, required percentage = $(\frac{{{\rm{Markedprice}} - {\rm{Costprice}}}}{{{\rm{Costprice}}}} \times 100\% )$

$( = \frac{{P\frac{{\left( {100 + y} \right)}}{{\left( {100 - x} \right)}} - P}}{P} \times 100\% = \frac{{x + y}}{{\left( {100 - x} \right)}} \times 100\% )$

Short trick Alternate method:-

When price of any article is increased by p% and then decreased by q% then net effect on the price of that article

⇒ Net Effect = $(p - q - \frac{{pq}}{{100}}\% )$ increment in the price.

In this case the net effect is a gain of y%.

And let the required percentage over the cost price is p and discount given on marked price is x%.

Then,

$(y = p - x - \frac{{px}}{{100}})$

⇒ 100y = p (100 – x) – 100x

$( \Rightarrow\ \ \ \ \ \ \ p = \frac{{100\left( {x + y} \right)}}{{\left( {100 - x} \right)}}\% )$