Three liquids of densities ρ1,ρ2 and ρ3 and heights as shown are in equilibrium in a U-tube. Match the columns.

At the bottom surface of liquid of density is ρ2ρ1gh+ρ3gK′h=ρ2ghρ3=gh⁡ρ2−ρ1K′gh=ρ2−ρ1K′ Compare with ρ3=2ρ2−ρ1 or K′=12K=K′h=h2So, required height of column of densityρ3=h2 Now compare with ρ3=ρ2−ρ12K′=2 or K=2hThus, required height of column of densityρ3=2h If  ρ1=ρ2,K'=03ρ2=3p1+ρ3 ⇒ρ3=3(ρ2−p1) or K'=13 ∴K=K'h=h3