Question 527848
A is 4 or less because A+A<10 (because the sum has only 3 digits, not 4).
When you add C+B in the ones' place the answer ends in A, but it must be 10+A, because the sum of the tens place (including a 1 possibly carried over) does not en in A, but ends in B.
So B+C=10+A for the ones
and B+C+1=10+B for the tens
That means that B=A+1
and A+A+1(carried over)=C
A=4, gives you B=5, and C=9, and that is one solution.
Is there another one?
If A<4, then B=A+1<4+1=5, and C=A+A+1=not more than 3+3+1=7
B+C<7+5=12=10+A, which would make A = 2 or less, but that would make
B=A+1<4, C=A+A+1=5 or less, and then B+C<9, which does not work.
So there is only one solution, the one listed above.