Let the two digit number be $xy.$ Its value in decimal is $10x + y.$
Then sum of two digits $=x+y=9 \quad \to(1)$
and $(10x+y)-45=10y+x$ $\{\because yx=10y+x\}$
$10x+y-10y-x=45$
$x-y=5\quad \to (2)$
From the equations $(1)$ and $(2),$ we get $x=7,y=2$
So, the number is $72$
Correct answer: (B).