Final Value Theorem yielding the wrong result?
Here is the FVT in Laplace domain \$-\$
$$\lim _{t\to\infty} H(t) = \lim _{s\to0}sH(s)$$
Transfer function is \$-\$
 $$H(s)=V_2(s) = V_1(s).\frac{5}{\frac{100}{10s+10}+5} $$
\$V_1\$ is a DC voltage source.
$$\implies V_2(s)=\frac{V_1}{s}.\frac{5}{\frac{100}{10s+10}+5}$$
@time = infinity,
$$ \lim _{s\to0}sH(s)=\lim _{s\to0}(s.\frac{V_1}{s}.\frac{5}{\frac{100}{10s+10}+5} )$$
$$=\frac{V_1}{3}$$