Let M₀ = mass of body in vacuum.
Apparent weight of the body in air=Apparent weight of standard weights in air 
⇒ Actual weight - upthrust due to displaced air = Actual weight - upthrust due to displaced air

$\Rightarrow {\text{M}}_0\text{g}-\left(\frac{{\text{M}}_0}{{\text{d}}_1}\right)\text{d}\text{g}=\text{M}\text{g}-\left(\frac{\text{M}}{{\text{d}}_2}\right)\text{dg}\Rightarrow {\text{M}}_0=\frac{\text{M}\left[1-\frac{\text{d}}{{\text{d}}_2}\right]}{\left[1-\frac{\text{d}}{{\text{d}}_1}\right]}$