iF 4a3b is divisible by 11 then the difference of sum of digits at odd place and sum of digits at even place is either 0 or divisible by 11

So, a + b - (4 + 3) or 4 + 3 - (a + b) must be zero or divisible by 11

=> a + b - 7 or 7 - (a + b) must be zero or divisible by 11

Case 1:

     a + b - 7 = 0

=> a + b = 7

Case 2:

     a + b - 7 = 11

=> a + b = 11 + 7

=> a + b = 18

Now, a + b - 7 can not be equal to -11 since a and b are positive integers.

Case 3:

7 - (a + b) = 0

=> a + b = 7

Case 4:

7 - (a + b) = 11

=> a + b = 7 - 11

=> a + b = -4

which is not possible.

So, we get the possible values of a + b as 7 and 18