The statement “The king was freed from his people and they from their king” is a comment made by Badauni on the death of Muhammad-bin-Tughlak, thus making option 3 the correct answer.

Elaborating on the options:

1. Balban: Although he was a significant figure in history, Badauni`s statement wasn`t related to him. He was known for his authoritative rule rather than his detachment from his people.

2. Ala-ud-din Khalji: He was an ambitious ruler well known for his market reforms and military campaigns, but again, Badauni did not make the statement in context of his death.

3. Muhammad-bin-Tughlak: This Sultan was known for his controversial decisions such as shifting the capital from Delhi to Daulatabad and introducing token currencies, which eventually led to a disconnect between him and his people. Badauni’s statement aptly describes this relationship, therefore, upon Muhammad-bin-Tughlak`s death, Badauni commented thus, signifying an end to an unpopular reign.

4. Feroze Shah Tughlak: Despite having a noteworthy rule, this statement isn`t associated with his death.

In conclusion, the focus is on the ruler`s relationship with his