The correct answer is option 'A', the Tughluq dynasty ruled for the longest period in the Delhi Sultanate.

The Tughluq dynasty, founded by Ghiyasuddin Tughluq, ruled over the Delhi Sultanate from 1320 to 1413. They were the third dynasty to rule over the Delhi Sultanate, following the Slave dynasty and the Khilji dynasty.

The Tughluq dynasty is known for its ambitious military campaigns, administrative reforms, and architectural endeavors. They expanded the empire to its greatest extent, reaching from the Indus River in the west to Bengal in the east, and from the Deccan Plateau in the south to the foothills of the Himalayas in the north.

Key Points:
- The Tughluq dynasty ruled for a total of 93 years, making it the longest-ruling dynasty in the Delhi Sultanate.
- Ghiyasuddin Tughluq was the founder of the dynasty and ruled from 1320 to 1325. He was succeeded by his son Muhammad bin Tughluq.
- Muhammad bin Tughluq is known for his ambitious expeditions, including the failed attempt to conquer the Deccan. He also introduced various administrative reforms, such as the token currency and the shifting of the capital from Delhi to Daulatabad.
- Muhammad bin Tughluq ruled from 1325 to 1351 and was succeeded by his cousin Firuz Shah Tughlaq.
- Firuz Shah Tughlaq is considered one of the most capable rulers of the dynasty. He focused on improving the infrastructure of the empire, constructing canals, reservoirs, and public buildings. He ruled from 1351 to 1388.
- The decline of the Tughluq dynasty began after the death of Firuz Shah Tughlaq. Weak successors, regional revolts, and external invasions led to the disintegration of the empire.
- The last ruler of the Tughluq dynasty was Nasir-ud-Din Mahmud Shah Tughlaq, who ruled from 1394 to 1413. He was overthrown by Khizr Khan, who founded the Sayyid dynasty.

In conclusion, the Tughluq dynasty ruled for the longest period in the Delhi Sultanate, from 1320 to 1413. They expanded the empire and undertook various administrative and architectural endeavors during their reign.

Tughluqs ruled for the longest which is 93 Years (1320-1413).