Find the values of the letters in the following and give reasons for the steps involved.
1 2 A + 6 A B
— — — — — — — — — — — — —
A 0 9

Lets assume, A+B>9
We know that A and B both can attain maximum value of 9,
If both A=B=9 then we get 18 where unit digit is 8, so its not possible to achieve unit digit as 9
This implies that sum must be =9
Now focusing on ten's digit, 2+A=0
Here, A has to be 8 as there is no carry over from unit digit addition.
Now, we know that A=8 ∴ B=9−A=9-8=1
Hence, A=8 and B=1.