A body weighs `W_(1)` in a liquid of density `rho_(1)` and `W_(2)` in a liquid of density `rho_(2)`. What is the weight of body in a liquid of density `rho_(3)`?

Explanation

let m be the mass of the body, V be its volume and `rho` be its density. So `V=m//rho`.
Weight of body in air, `W=mg`.
Effective weight of the body when completely immersed in a liquid of density `rho_(1)` is
`W_(1) = mg - V rho_(1) g =mg - (m)/(rho) rho_(1)g`
`= mg(1-(rho_1)/(rho))=W(1-(rho_1)/(rho))` ...(i)
similarly, `W_(2) = W(1-(rho_2)/(rho))` ..(ii)
and `W_(3) = W(1-(rho_3)/(rho))` ..(iii)
Using (i),(ii) and (iii) , we get
`W_(3) = W_(2) (rho_(3)-rho_(1))-W_(1)(rho_(3)-rho_(2))/(rho_(2)-rho_(1))`.