People add sodium chloride to water while boiling eggs. This is to:

Increase the boiling point of water

When a non-volatile solute, such as salt (sodium chloride), is added to water, it increases the boiling point of the water. This phenomenon is known as boiling point elevation.

By increasing the boiling point of the water, the addition of salt can indeed help the eggs cook sooner. The higher boiling point means that the water needs to reach a higher temperature to boil, which leads to faster and more efficient heat transfer to the eggs. As a result, the eggs cook more quickly compared to boiling them in pure water.

Therefore, the addition of a non-volatile solute like salt to water increases its boiling point, which can help the eggs cook sooner.