A concave mirror with a radius of curvature of 40 cm is positioned...

Given, radius of curvature of the concave mirror, $R = -40 \text{ cm}$

Focal length, $f = \dfrac{R}{2} = -20 \text{ cm}$

Object distance, $u = -30 \text{ cm}$

Using the mirror formula:

$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$

$\dfrac{1}{v} + \dfrac{1}{-30} = \dfrac{1}{-20}$

$\dfrac{1}{v} = \dfrac{1}{30} - \dfrac{1}{20}$

$\dfrac{1}{v} = \dfrac{2 - 3}{60} = -\dfrac{1}{60}$

$v = -60 \text{ cm}$

The negative sign indicates that the image is formed in front of the mirror, which is on the same side as the object. Therefore, the image is located $60 \text{ cm}$ from the mirror on the side of the object.