The authority that recommends the principles governing the grants-in-aid of the revenues to the states out of the Consolidated Fund of India is the Finance Commission.

The Finance Commission is a constitutional body in India that is constituted by the President of India every five years or at any interval as deemed necessary. The primary function of the Finance Commission is to recommend the distribution of financial resources between the central government and the state governments.

One of the important aspects of the Finance Commission`s role is to recommend the principles and criteria for providing grants-in-aid to the states from the Consolidated Fund of India. These grants-in-aid are aimed at supporting the states in meeting their fiscal requirements, promoting balanced regional development, and addressing any fiscal imbalances between different states.

Therefore, it is the Finance Commission that recommends the principles governing the grants-in-aid of the revenues to the states out of the Consolidated Fund of India.