Let the smaller digit = x
Then since the digits are consecutive,
the larger is 1 more than the smaller digit,
So the larger digit = x+1
if the digits are interchanged. the original value is increased...
That tells us that the original number is smaller than the
number with the digits interchanged. So the original number
has the smaller first (or tens) digit. Therefore:
The original number = 10x + (x+1)
The number with the digits reversed = 10(x+1) + x
if the digits are interchanged. the original value is increased by 9
10(x+1) + x = 10x + (x+1)
Solve that for x and what you get for x will be the smaller digit,
then add 1 to it and what you get will be the larger digit. You
finish.
Edwin
