Solution:
Let the mean proportion be $x$.
Then, $4: x:: x: 25$
$$
\begin{array}{l}
\Rightarrow \quad \frac{4}{x}=\frac{x}{25} \\
\Rightarrow \quad x^{2}=4 \times 25=100 \\
\therefore \quad x=\sqrt{100}=10 ; \text { Ans. }
\end{array}
$$
$\therefore \quad$ Correct option is $(b)$
Trick :
Mean Proportion
$$
=\sqrt{a b}=\sqrt{4 \times 25}=10 \text {; Ans. }
$$