Mr. Someone

A horse worth $900 is sold by A to B at 10% loss and B sells the horse back to A at 10% profit, then the result is--- A.A loss $9 B.B loss $9 C.neither loss nor gain D.none The answer in the book in the answer key is (a) but I keep getting 171 as the loss...

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What I think I am doing wrong is 1st case-- A sells it to B at 10%loss i.e. at 810 Now he has lost 90$ here 2nd case B sells the horse worth $810 at 10% profit i.e around $891 So A has lost almost $81 here as well. So, how could A have lost just $9???

The initial CP of the horse (for A) is $900 And he buys it next time at $891. How has he lost $9 here?