Who founded the Prarthana Samaj in Mumbai in 1867?

The correct answer is Atmaram Pandurang.

Step-by-step Explanation:
1. Context and Origin: Prarthana Samaj (meaning "Prayer Society" in Sanskrit) was a movement for religious and social reform in Mumbai (formerly Bombay), India. It was founded during the Bengal Renaissance period as a reform movement aimed at reforming Hindu religious and social practices.
2. Foundation: The society was established on 31 March 1867. It was founded by Dr. Atmaram Pandurang, a physician and social reformer, along with his brother Dadoba Pandurang and other prominent reformers like Justice Mahadev Govind Ranade (who joined later and helped expand its reach) and R. G. Bhandarkar.
3. Core Philosophy: The movement was heavily inspired by the Brahmo Samaj (founded by Raja Ram Mohan Roy) but chose to remain within the fold of Hinduism, focusing on monotheism, the worship of one God, and opposing caste discrimination, child marriage, and the denial of education to women.
4. Analyzing the Options:
- Gopal Krishna Gokhale: Founded the Servants of India Society in 1905.
- Shri Ram Bajpai: Associated with the Seva Samiti (founded in Allahabad in 1914).
- Atmaram Pandurang: Successfully founded the Prarthana Samaj in 1967.
- Raja Ram Mohan Roy: Founded the Brahmo Sabha (later Brahmo Samaj) in Calcutta in 1828.