Radius of curvature of concave mirror is 40 cm and the size of image is twice as that of object, then the object distance is : 

30 cm

Use : \(\frac{1}{f}\) = \(\frac{1}{v}\) + \(\frac{1}{u}\) 

$ f = \frac{R}{2} = -20cm$

Magnification is twice, image can be real or virtual.

Case 1: Image is Real 

$ M = 2 = -\frac{v}{u} \Rightarrow v = -2u$

$ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} = \frac{1}{-2u} + \frac{1}{u} = \frac{1}{2u}$

$\Rightarrow u = \frac{f}{2} = -10cm$

Case 2: Image is virtual 

$ M = - 2 = -\frac{v}{u} \Rightarrow v = 2u$

$ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} = \frac{1}{2u} + \frac{1}{u} = \frac{3}{2u}$

$\Rightarrow u = \frac{3f}{2} = -30cm$