A body weighs W₁ in a liquid of density p₁ and W₂ in a liquid of densith p₂. What is the weight of body in a liquid of density p_3.

p = rho

let actual weiight of body is W & volume is V then

 W - p₁V._g = W_{1       ........1}

 W - p₂Vg = W₂     ........2

solving  1 & 2

 W =  (W₁p₂-W₂p₁)/p₂-p₁        &         V = (W₁-W₂)/g(p₂-p₁)

now , let its weight in liquid P₃ is W₃ then

 W - p₃V.g ₌ W₃

now putting V & W ,

 we get

 W₃ = [W₁p₂-W₂p₁-p₃(W₁-W₂)]/(p₂-p₁)

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