When the object is at distance u₁ and u₂ from a lens, a real image and virtual image are formed respectively having the same magnification. The focal length of the lens is: 

Utilize the lens formula and the magnification formula to get the focal length of the lens in the solution, equating the lens magnification for the two pictures.
According to the information provided, m and -m will be the generated magnification.

u₁ = f(1+$\frac{1}{m}$)

u₂ =  f(1-$\frac{1}{m}$)

On solving above both expressions (Eliminating m ) we get:

$f = \frac{u_{1 }+ u_2}{2}$

Hence, the correct answer is option C.