If a two digit number increases by 54 when the digits are reversed, what is the number?

If a two digit number increases by 54 when the digits are
reversed, what is the number.

Let the 2 digits in order be
x and y.

Then the value of the number =
10x+y.

When the digits are reversed , the digits in order
are y and x.

So the valuse of the number is
10y+x.

Since 10y+x -(10x+y) =
54,

9y -9x = 54.

Or  y-x=
6.

Therefore y = x+6.

So the
digits in the solution are  when x= 1, y = 1+6 = 7.

When
x=2, y = 2+6 = 8.

When x= 3, y = 3+6 = 6 =
9.

Therefore there are 3 solutions : 17 ;  28 and  39
which, when reversed, become 71 ;  82 and  and 93 each increase by  54 after reversing
the digits.