When an object of mass 200g is submerged in methanol, its apparent weight is 1.052N. When submerged in benzene its apparent weight is 0.951N. If the density of methanol is 0.8g/cm^3, What is the density of benzene?

When the object is submerged in methanol, it displaces an amount of methanol with weight 1.052 N, i.e. with mass = (1.052 N)/g ≈ 107.347 g. With a density of 0.8 g/cm³, this means the displaced methanol and hence the object itself have a volume of

v ≈ (107.347 g) / (0.8 g/cm³) ≈ 134.184 cm³

Likewise, when submerged in benzene, the object displaces 0.951 N of benzene, whose mass is (0.951 N)/g ≈ 97.041 g with the same volume as the object. So the density d of benzene is

d ≈ (97.041 g) / (134.184 cm³) ≈ 0.723 g/cm³