The sum of the digits of a two digit number is 9. the number formed by interchanging the digits is 27 less than the original number. find the original number and its reversal

x + y = 9   equation 1 the sum of the digits of a two-digit number is 9

the number formed by interchanging the digits is 27 less than the original number
 we are looking at the number  xy,
 10x+y for x is a tens digit.
10y + x = 10x + y + 27
simplify it, 
9y = 9x + 27  divide by 9

x + y = 9   equation 1
y= x + 3    equation 2  

by subtitution   we put y in equation 1

x   + (x+3) = 9
 2x = 6 
x= 6/2= 3   

 y = x+3=3+3=6

If you make it a little more clear i can answer it