cost price of item

cost price of item

let us consider following problem:
Roger sold a watch at a profit of $10$%. If he had bought it at $10\%$
less and sold it for $13$ dollar less,then he would have made a profit of
$15$%. What is the cost price of the watch?
suppose that price of watch is $x$ dollar, $profit=sell -cost $
so let us denote price of watch by $x$,then if he would buy it $10$
less,then cost of this would be $x-0.1*x=0.9*x$, and if it sold $13$
dollar less,then sold price would be $x-13$, profit is $15$%,then it would
be $0.15*x$ right? or we have
$(x-13)-0.9*x=0.15*x$
but it makes negative equation like $13=-0.05*x$,so what is my mistake,how
can i used information like Ronger sold watch at a profit of $10\%$?
Thanks in advance