A lens forms a real image of an object. The distance from the object to the lens is x cm and that from the lens to the image is y cm. the graph (Fig.) shows the variation of y with x.

It can be deduced that the lens is

A diverging lens if ruled out because both x and y are positive values. Both x and y equal 20 cm at their smallest sum, which occurs when
x + y = 40 cm = 4 f 
$\therefore$ f =  10 cm
This indicates a converging lens of focal length = 10 cm