Question 729530
Let this two digit number be {{{10*x+1*y}}}.
The digit reversal of the number would be {{{10*y+1*x}}}.


The ratio as stated gives the proportion, {{{highlight((10x+1)/(x+10y)=2/9)}}}.
The sum of the digits being 9 means {{{highlight(x+y=9)}}}.


Now that the conversion into symbolism and equations has been made, most of the problem, the harder part, is solved.  Merely solve the resulting system for x and y.