If the product of two numbers is $$360$$ and their ratio is $$10 : 9$$, then find the numbers.
Let the two numbers be $$10x$$ and $$9x$$.
Product of the two numbers = $$360$$
$$\therefore 10x*9x=360$$
$$\Rightarrow 90x^{2}=360$$
$$\Rightarrow x^{2}=4$$
$$\Rightarrow x=2$$
$$\therefore$$ One number = $$10x$$ = $$10*2$$ = $$20$$
Other number = $$9x$$ = $$9*2$$ = $$18$$
Thus, the two numbers are $$18$$ and $$20$$