A uniform shop sign is 2.4 m long and is held horizontally by a hinge on a wall at one end. The sign weighs 90 N, with its weight acting 1.2 m from the hinge. A vertical chain at the other end pulls upwards on the sign with a force of 120 N. A lantern weighing 180 N is to be hung from the sign. At what distance from the hinge must the lantern be hung so that the sign is in rotational equilibrium?
1.0 m1.0\ \mathrm{m}1.0 m
1.6 m1.6\ \mathrm{m}1.6 m
0.60 m0.60\ \mathrm{m}0.60 m
0.40 m0.40\ \mathrm{m}0.40 m