Permanent hardness of water may be removed by the addition of:
A. Sodium carbonate
B. Alum
C. Potassium permanganate
D. Lime

Hint: Solve this question by keeping in mind the causes of permanent hardness of water and the reaction it needs to undergo to remove to hardness causing elements.

Complete step by step answer:
Permanent hardness of water is caused because of the presence of calcium and magnesium ions. Therefore, a substance that can remove these ions will be the answer.
Amongst the given options, sodium carbonate can solve the purpose. Sodium carbonate is water soluble in nature and hence, adds a large amount of carbonate ions to the water.
Sodium Carbonate - \[N{{a}_{2}}C{{O}_{3}}\], is the disodium salt of carbonic acid and has an alkalinizing property. When dissolved in water, sodium carbonate forms carbonic acid and sodium hydroxide. The reaction is as follows –
\[N{{a}_{2}}C{{O}_{3}}+{{H}_{2}}O\to N{{a}_{2}}O+{{H}_{2}}C{{O}_{3}}\to 2NaOH+{{H}_{2}}O+C{{O}_{2}}\]
Calcium and magnesium ions in water react with it to produce insoluble precipitates. Sodium carbonate is soluble but calcium carbonate and magnesium carbonate are insoluble. These react with dissolved calcium ions, to form a precipitate of calcium carbonate:
\[C{{a}^{2+}}\left( aq \right)\text{ }+\text{ }C{{O}_{3}}^{2}\left( aq \right)\text{ }\to \text{ }CaC{{O}_{3}}\left( s \right)\]
(there is a similar reaction for magnesium ions)
In the above reaction, the calcium ions come from hard water and the carbonate ions from the sodium carbonate. And thereby, hardness is removed.
Therefore, the answer is option (a) – Sodium carbonate.

Note: Sodium carbonate is also known as washing soda. Do not confuse it with Sodium bicarbonate, which is also known as baking soda. It can soften temporary hardness of water and it softens water that has permanent hardness.