When an object is placed at a distance of 60cm from the convex mirror the magnification produced is 0.5. where should the object be placed in order to obtain magnification of .33

In case of convex mirror,

In the first part, u=-60cm ,

m=1/2 implies v=30 cm (Since the image must bevirtual)

onlSubstituting in eqn

or 

we get f = 60 cm

In II case

m=1/3=0.33

m=-(v/u)

v=-u/3

f=60cm

substituting in

we get u=-2f=(-2)x 60cm =-120cm