Step 1: Compare the object distance with the focal length.
The focal length is $f = 30\text{ cm}$, so the centre of curvature is at $2f = 60\text{ cm}$, and the object is placed exactly at $u = -60\text{ cm}$, which is exactly at the centre of curvature.
Step 2: Recall the special property of the centre of curvature.
Whenever an object sits at the centre of curvature of a concave mirror, the reflected rays retrace a symmetric path and meet again at that same point, so the image also forms right at the centre of curvature.
Step 3: Confirm with the mirror formula. \[ \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{-30} - \frac{1}{-60} = -\frac{2}{60}+\frac{1}{60} = -\frac{1}{60} \implies v = -60\text{ cm} \] This matches our expectation, the image is $60\text{ cm}$ in front of the mirror.
Step 4: State where to place the screen.
Since the image is real, it can be caught on a screen placed at that very spot.
\[ \boxed{60.0\text{ cm in front of the mirror}} \]