Question

Find the values of the letters in the following and give reasons for the steps involved.
$12A\underset{–}{+6AB}\underset{–}{A09}$

Answer 1

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 $A=8$

$\therefore B=9-A=9-8=1$

Hence, $A=8$ and $B=1$.