Let v be the object's volume. The object displaces 0.4v cm³ of water, which, at a density of about 0.997 g/cm³, has a weight of
b = (0.000997 kg/cm³) (0.4 v cm³) g ≈ 0.000391v N
(and b is also the magnitude of the buoyant force). Then the net force on the object while it's floating in water is
∑ F = b - mg = 0
so that b = mg, where mg is the object's weight. This weight never changes, so the object feels the same buoyant force in each liquid.
(a) In methanol, we have
b = 0.000391v N = (0.00079 kg/cm³) (pv cm³) g
where p is the fraction of the object's volume that is submerged. Solving for p gives
p = (0.000391 N) / ((0.00079 kg/cm³) g) ≈ 0.0505 ≈ 5.05%
(b) In carbon tetrachloride, we have
b = 0.000391v N = (0.00158 kg/cm³) (pv cm³) g
==> p ≈ 0.0253 ≈ 2.53%
