The original number: 10a + b (a and b are each single digits from the set {'0','1',...,'9'}
Reversing the digits gives the number 10b + a
Swapped number = 2(Original number) - 1:
10b + a = 2(10a + b) - 1
Because a+b=10, we can replace 'a' with '10-b' to get one equation in one unknown (in this case, b):
10b + (10-b) = 2(10(10-b) + b) - 1
...
This simplifies to b=7 ==> a=3
The original number is 37
The swapped number is 73
Check:
73 = 2(37)-1 = 74-1 (ok)