Two  bodies with volumes V and 2V are equalized on a balance. The larger body is then immersed in oil of density = 0.9 g/cc. what must be the density of the liquid in which the smaller body simultaneously immersed so as not to disturb the equilibrium of the balance ?

Given:

V₁ = V
V₂ = 2 V
both have the same mass.  

Therefore, their densities are,
M₁ = M₂      and    d₂ = ½ × d₁
M₂ is immersed in oil of density 0.9 g/cc
Buoyancy force on the larger body, M₂ =  V₂ × 0.9 × g 

let the density of the liquid in which the smaller body M₁ is immersed be  d g/cc
Buoyancy force on the smaller body,  M₁ =  V₁ × d × g
 For the balance to remain at equilibrium,    M₂ = M₁

 V₂ × 0.9 × g = V₁ × d × g

The density of the liquid in which the smaller body simultaneously immersed is 1.8 g/cc