A man bought an article for $360. At what price must he mark the articles so that he can allow a discount of 10% and still make a profit of 10% of the cost price?

You want
  (marked price) - 10%*(marked price) = (cost price) + 10%*(cost price)
  .90*(marked price) = 1.10*(cost price)    [convert to decimals]
  (marked price) = 1.10/.90*(cost price)    [divide by .90]
  (marked price) = 1.10/.90*360
  (marked price) = 440

The man will mark the article at $440. He can allow a discount of $44, 10% of the marked price, and expect the sale to occur at a price of $396, which is $36 above his cost, a profit of 10%.