The image of the object can be located on the screen for two positions of convex lens such that u and v are exchanged.
The separation between two positions of the lens is x = 20 cm.

It can be observed from figure.
u1+v1 = 90 ...(i)
v1–u1 = 20 ...(ii)
Solving equation (i) and equation (ii)
v1 = 55 cm, u1 = 35 cm
Now lens formula,

1

v

−

1

u

=

1

f

1

55

−

1

−35

=

1

f

or

1

55

+

1

35

=

1

f

35+55

55×35

=

1

f

or f =

55×35

90

= + 21.38 cm