Ages of person A and B

$A - 7 = 7(B - 7)$

$A - 7 = 7B - 49$

$A = 7B - 42$ $[1]$

$A + 3 = 3(B + 3)$

$A + 3 = 3B + 9$

$A = 3B + 6$ $[2]$

Substitute the value $A$ in $[1]$ to $[2]$ .

$A = A$

$7B - 42 = 3B + 6$

$4B = 48$

$\color{#3D99F6}\boxed{B = 12}$

Let the ages of person A and B be $a$ and $b$ respectively. Then

$\begin{cases} a-7 = 7(b-7) & \implies a = 7b - 42 \\ a+3 = 3(b+3) & \implies a = 3b + 6 \end{cases}$

$\begin{aligned} \implies 7b-42 & = 3b+6 \\ 4b & = 48 \\ \implies b & = \boxed{12} \end{aligned}$

Let the present ages of $A$ and $B$ be $a_A$ and $a_B$ respectively. Then $a_A-7=7(a_B-7)\implies a_A=7a_B-42$ . And $a_A+3=3(a_B+3)\implies a_A=3a_B+6$ . From these two, we get $3a_B+6=7a_B-42\implies a_B=\boxed {12}$ .