The correct answer is option 1, Ghanshyam Das Birla. He was an Indian businessman who believed in the concept of "healthy capitalism" and supported Mahatma Gandhi in his efforts to work towards a common goal. Birla believed that business should not solely focus on profit-making, but also contribute to the welfare of society. He actively participated in the Indian independence movement and used his resources and influence to support Gandhiji and other leaders.

Option 2, Ambalal Sarabhai, was also a prominent Indian businessman and philanthropist, but there is no specific information available about his support for Gandhiji or his views on capitalism.

Option 3, Sir Biren Mookerjee, was an industrialist and politician, but there is no evidence to suggest that he supported Gandhiji or had similar beliefs about capitalism.

Option 4, T. T. K. Krishnamachari, was a politician and economist, but there is no information available about his views on capitalism or his support for Gandhiji.

In conclusion, the Indian businessman who favored "healthy capitalism" in helping Gandhiji to work towards a common object was Ghanshyam Das Birla.