After giving a discount of 30% on an article, a trader made a profit of 20%. If the trader had given a discount of rs 400, he would have incurred a loss of 20%. find the marked price of the article.

Let the actual cost of the article be x
And the selling price be y .
Now if discount is 30%
Then the discounted selling price is .7y.
the profit is then (.7y-x)*100/x.
Now this is 20%
Hence 70y-100x=20x
or 70y=120x....(i)
Also if the discounted selling price is y-400
Then the loss is( x-y+400)*100/x.
Which is given as 20%
Hence 100x-100y+40000=20x
or,-80x+100*120x/70=40000 from i
or -8x+120x/7=4000
or,64x/7=4000
x=437.5