We can write
n = 10a + b
where a and b belong to {1, 2, 3, …, 9}.
Swapping the digits produces a new number
n' = 10b + a
and adding 3 to this number makes up 2n,
n' + 3 = 2n
or
(10b + a) + 3 = 2 (10a + b)
so that
19a - 8b = 3
Since we want n to be the smallest possible 2-digit number that meets the criteria, let's start with a = 1. Then solving for b, we find
19 - 8b = 3
16 = 8b
b = 2
So, the number we're looking for is n = 12.
Just to confirm, swapping the digits gives 21, and 21 + 3 = 24 = 2•12.
