Concept:
The nineteenth century in India witnessed a powerful intellectual wave known as the Indian Reissance. Several thinkers sought to cleanse Hindu society of obsolete superstitions and degrading customs while drawing spiritual rejuvetion from ancient scriptures.
Step 1: Correlating the attributes to the correct reformer
• Opposed child marriage and advocated social justice: The reformer actively fought against retrograde patriarchal practices, working to uplift margilized sections and women.
• Campigned for reform of Hinduism: He highlighted that real Hinduism does not support untouchability or empty rituals, but emphasizes inner spiritual strength and service to humanity ("Daridra raya").
• Known for Vedantic theory: This is the definitive clue. Swami Vivekanda championed Neo-Vedanta (Practical Vedanta), presenting the ancient Advaita Vedanta philosophy in a modern, ratiol form at the 1893 Parliament of Religions in Chicago.
Step 2: Checking other reformers
• Jyotiba Phule: Famously founded Satyashodhak Samaj; worked for lower-caste education, but did not operate within Vedantic philosophy frameworks.
• M.G. Rade: Connected with Prartha Samaj, worked heavily on economic tiolism and social reform, but is not primarily identified with Vedantic philosophy.
• Gopal Hari Deshmukh ("Lokhitwadi"): Wrote critical essays against orthodox traditions, but did not focus on Vedantic revival.
Thus, Swami Vivekanda is the correct match.