4.

\( \;\;\begin{array} \hline \;\;\;A & B\\ +\;3& 7\\ \hline \;\;6 & A\\ \hline \end{array} \)

\( \;\;\begin{array} \hline \;\;\;A & B\\ +\;3& 7\\ \hline \;\;6 & A\\ \hline \end{array} \)

We have here two conditions :

(i) B+7=A

(ii)A+3=6

By solving the second equation we get A=6-3=3

Also if we keep A=3 directly in eq. (i) we get B=3-7=negative value. So it can be said that a carry was taken so let the carry be 1.Therefore, now A=2+1(carry) and let us check if eq. (i) satisfies it or not.

We have B+7=12[∵ 1(carry)2(value of A)]

So we get B=12-7=5.

So the sum becomes :

\( \begin{array}
\hline
\;\;\;2 & 5\\
+\;3& 7\\
\hline
\;\;6 & 2\\
\hline
\end{array}
\)

Hence, the assumption is correct and values are A=2 and B=5