SOLUTION: The sum of the digits of a certain two-digit number is 10. If the digits are reversed, a new number is formed which is one less than twice the original number.

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)