Question

The difference between the two digits of a two digit number is 2. If the digits swap places,the number is 18 less than the original number. What is the original number?

Answer 1

let the tens digit be x, then the unit digit is x-2
x ≥ 2

the value of the number is 10x + x-2
the value of the number reversed is 10(x-2) + x

10x + x-2 - ( 10(x-2) + x) = 18
11x - 2 - (11x - 20) = 18
11x - 2 - 11x + 20 = 18
18 = 18 , which is a true statement.
So it will work for any number of x
and the original number could have been:
20, 31, 42, 53, 64, 75, 86, or 97

check:
20 - 02 = 18
31 - 13 = 18
42 - 24 = 18
53 - 35 = 18
...
97 - 79 = 18

Answer 2

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Thx