Comparing Quantities — MATHS STD 7 — Question

Let the third proportional of $3$ and $27$ be $x.$
Then,
$3:27::27:\text{x}$
$\Rightarrow3:27=27:\text{x}$
$\Rightarrow\frac{3}{27}=\frac{27}{\text{x}}$
$\Rightarrow3\text{x}=27\times27$
$\Rightarrow\text{x}=\frac{27\times27}{3}$
$\Rightarrow\text{x}=27\times9$
$\therefore\text{x}=243$
So, the third proportional of $3$ and $27$ is $243.$
Hence, the correct alternative is option $(a).$