Jainism, buddhism, and hinduism all emerged in india in this period. how did each one appeal to people? did each one appeal to different groups of people? why? how did their popularity develop through this period?

Buddhism and Jainism were attracted to the lower classes. They gain popularity because leaders spread Buddha beliefs, for example, Jainism became popular when Vardhamana Mahavira turned to it. Hinduism appealed to the Gupta emperors and it became popular through the telling of epics.

These three religions, Jainism, Buddhism, and Hinduism have many similarities, and also particular differences, among them, Jainism and Buddhism are based on the Sramana system in which their gods are not considered the creators; and humans are capable to experience the highest spiritual state as “Siddharta Gautama” did most known as “The Buddha” after meditating for days became enlightened.

Jains and Buddhists believe in penance, nonviolence and meditation as a path to self control.

The goal of a Buddhist or Jain is reaching Nirvana (the perfect peace) enlightenment, and immortality with no suffering or pain

And Hinduism is based on the Brahmana system where the gods are the creator, the preserver and the destroyer, similar to the God in Christianity, where God is powerful and judges everything.  

Everything done by the Hindus is related to their gods, they believe that "God is the universe, and the universe is God."  

Hindus are divided in groups (or a caste system), each group has a duty determined by “karma” (the sum of somebody’s actions in previous lives determining his future fate), the higher the class, the closer to nirvana or heaven.

Hindus have 4 main rankings in the caste system: Brahman (priest), Kshatriya (warrior), Vaisya (merchant/ farmer), and Sudra (worker), they also have a group called Delit or (Untouchables), but often not considered part of the caste system.  

Most of what the Hindus believe in are fairly realistic and affects their lives daily, such as the caste system.

Among their similarities, all three have the life-cycle and the need of liberation, worshiping one central deity that was human before and gained enlightenment; they also recognize the existence of the eternal soul and re-incarnation after-death.

Hinduism is considered the world's oldest religion, and it’s the most popular system in India with approximately 80% of the population.

Jainism and Buddhism make approximately 6 to 7% in popularity since they engaged their traditions and beliefs, although Jainism originated first.