Hint: Use the magnification formula of the compound microscope.

Step 1: Find the angular magnification of the eyepiece.
The total magnifying power of the compound microscope, m = 30
The angular magnification of the eyepiece is given by:

${\mathrm{m}}_{\mathrm{e}}=\left(1+\frac{\mathrm{d}}{{\mathrm{f}}_{\mathrm{e}}}\right)=\left(1+\frac{25}{5}\right)=6$

Step 2: Find the magnification of the objective lens.
The angular magnification of the objective lens (m_o):

${\mathrm{m}}_{\mathrm{o}}=\frac{\mathrm{m}}{{\mathrm{m}}_{\mathrm{e}}}=\frac{30}{6}=5$

Also, the magnification of the objective is given by:

Step 3: Find the position of the image for the objective lens.
Applying the lens formula for the objective lens:

The object should be placed 1.5 cm away from the objective lens to obtain the desired magnification.

Step 4: Find the object distance for the eyepiece.
For the eyepiece:

Object distance, ${\mathrm{u}}_{\mathrm{e}}=?$

Image distance, ${\mathrm{v}}_{\mathrm{e}}=-\mathrm{D}=-25 \mathrm{cm}$

Applying the lens formula:

$\frac{1}{{\mathrm{u}}_{\mathrm{e}}}=\frac{1}{{\mathrm{v}}_{\mathrm{e}}}-\frac{1}{{\mathrm{f}}_{\mathrm{e}}}$
$=\frac{-1}{25}-\frac{1}{5}=-\frac{6}{25}$
$\Rightarrow {\mathrm{u}}_{\mathrm{e}}=-4.17 \mathrm{cm}$

Step 5: Find the separation between the objective lens and the eyepiece.
The separation between the objective lens and the eyepiece $=\left|{\mathrm{u}}_{\mathrm{e}}\right|+\left|{\mathrm{v}}_{\mathrm{o}}\right|=4.17+ 7.5=11.67 \mathrm{cm}$

Therefore,  the separation between the objective lens and the eyepiece. should be 11.67cm