10.

\(\;\; \begin{array} \hline \;\;\;1 & 2 &A\\ + 6 & A&B\\ \hline \;\;A&0 & 9\\ \hline \end{array} \)

\(\;\; \begin{array} \hline \;\;\;1 & 2 &A\\ + 6 & A&B\\ \hline \;\;A&0 & 9\\ \hline \end{array} \)

We have condition as:

(i)A+B=9.

(ii)2+A=10.

(iii)1+6+1(carry)=A

We can say by equation (iii) and equation (ii) that A=8

Also, we have A+B=9. Sustituting A=8, we get B=1

Hence, we have A=8 and B=1