If 27, 36, 'x' are in continued proportion, then the value of 'x' from the following choice is:

It is given that the numbers 27, 36, x are in continued proportion.

We have to find the value of x.

Apply condition for continued proportionality,

$\mathrm{a}:\mathrm{b}::\mathrm{b}:\mathrm{c}$

$\frac{\mathrm{a}}{\mathrm{b}}=\frac{\mathrm{b}}{\mathrm{c}}$

Substitute the known values within the formula

$\frac{27}{36}=\frac{36}{\mathrm{x}}$

$\Rightarrow \mathrm{x}=\frac{36\times 36}{27}$

By solving the above equation,

$\Rightarrow \mathrm{x}=12\times 4$

$\Rightarrow \mathrm{x}=48$

Therefore, the value of 'x' is 48.