The correct answer is "Participation of workers in the management of industries" and it was added to the Directive Principles of State Policy by the 42nd Amendment to the Indian Constitution.

Here is an explanation of all the options:

Option 1: "Equal pay for equal work for both men and women". This principle is already an integral part of the Indian Constitution and was not added by the 42nd amendment.

Option 2: "Participation of workers in the management of industries". This principle was indeed added to the Directive Principles of State Policy by the 42nd amendment.

Option 3: "Right to work, education and public assistance". This is covered under different articles in the Indian Constitution and was also not added by the 42nd Amendment.

Option 4: "Securing living wage and human conditions of work to workers". Similar to option 1, this principle is already contained in the constitution and was not added by the 42nd amendment.

Thus, the correct answer is option 2, the principle of "Participation of workers in the management of industries".