Let the numbers be \(x\) and \(y\)
\begin{aligned}
&x: y=3: 7 \\
&\frac{x}{y}=\frac{3}{7}, x=\frac{3 y}{7} \ldots(1) \\
&x-12
\end{aligned}
\(\frac{x-12}{y-12}=\frac{9}{37} \ldots \ldots(2)\)
Put eqn (1) into eqn (2)
\begin{aligned}
&\frac{3 y}{7}-12 \\
&\frac{7}{y-12}=\frac{9}{37} \\
&\frac{3 y-84}{7(y-12)}=\frac{9}{37} \\
&\frac{3 y-84}{7 y-84}=\frac{9}{37} \\
&37(3 y-84)=9(7 y-84) \\
&111 y-3108=63 y-756 \\
&111 y-63 y=-756+3108 \\
&48 y=2352, y=\frac{2352}{48}=49 \quad \text { }
\end{aligned}