what is C?

[sanju09]

A B
+
C D
______
A A A
______

In the correctly done addition work above, A B and C D are two distinct 2-digit numbers and their sum, A A A, is a 3-digit number. If A, B, C, and D are distinct digits, what is C?

[karmayogi]

1. What's the maximum sum of any two different digits?
9 + 8 = 17

We can conclude two things from #1
A. The maximum carry forward (F) possible is 1
B. A has to be 1 because 11 is the only possible value of A + C + F = AA

B + D = F + 1
Now, either F = 1 or 0. F can't zero because for that B and D has to be 1 and 0 or vice versa.

Now,

1 + C + 1 = 11
C =9 ANSWER