The correct option is A Clarke's method
In Clarke's method some lime is added to the water which precipitate the Ca(HCO3)2 and Mg(HCO3)2 as CaCO3 and Mg(OH)2 respectively. So, this method used to remove temporary hardness.
Permanent hardness is shown due to the presence of soluble salts of magnesium and calcium in the form of chlorides and sulphates in water.
Washing soda reacts with soluble calcium and magnesium chlorides and sulphates in hard water to form insoluble carbonates.
Sodium hexametaphosphate Na6P6O18, commercially called ‘calgon’, when added to hard water, the following reactions take place
Na6P6O18→2Na++[Na4P6O18]2−M2++[Na4P6O18]2−→[Na2MP6O18]2−+2Na+
Here M=Mg,Ca
The complex anion keeps the Mg2+ and Ca2+ ions in solution.
In ion exchange method, the exchange reaction takes place to remove Mg2+ and Ca2+ to remove permanent hardness.