A Galilean telescope measures 27 cm in length when it is focussed...

For a Galilean telescope in normal adjustment (image at infinity), the length of the telescope tube is given by the difference between the focal length of the objective and the magnitude of the focal length of the eyepiece.

$L = f_o - f_e$

Given that the length of the telescope $L = 27 \text{ cm}$ and the focal length of the objective $f_o = 30 \text{ cm}$.

Substituting the given values:

$27 = 30 - f_e$

$f_e = 30 - 27 = 3 \text{ cm}$

The focal length of the eyepiece is $3 \text{ cm}$.