The correct answer is option 'A', the Finance Commission.

Explanation:
The Finance Commission is the authority that recommends the principles governing the grants-in-aid of the revenues to the states out of the Consolidated Fund of India. Let's understand this in detail:

1. Finance Commission:
The Finance Commission is a constitutional body established under Article 280 of the Indian Constitution. It is appointed by the President of India every five years or at such earlier time as deemed necessary. The primary responsibility of the Finance Commission is to recommend the distribution of financial resources between the Union government and the state governments.

2. Grants-in-Aid:
Grants-in-aid are the funds provided by the Union government to the state governments to supplement their own resources. These grants help the states in meeting the expenditure requirements for various purposes like infrastructure development, social welfare programs, education, healthcare, etc.

3. Consolidated Fund of India:
Consolidated Fund of India is a fund created under Article 266 of the Indian Constitution. It includes all revenues received by the government (tax revenue, non-tax revenue, capital receipts, etc.), as well as loans raised by the government. The money from this fund is used to meet the general expenses of the government.

4. Principles governing grants-in-aid:
The Finance Commission recommends the principles governing the grants-in-aid of the revenues to the states out of the Consolidated Fund of India. These principles are based on various factors such as population, area, income disparities, fiscal capacity, and other relevant factors. The aim is to ensure a fair and equitable distribution of resources among the states.

5. Other options:
a) Inter-State Council: The Inter-State Council is a constitutional body established under Article 263 of the Indian Constitution. It is responsible for discussing and resolving issues of common interest between the Union government and the state governments. However, it does not recommend principles governing grants-in-aid.
c) Union Ministry of Finance: While the Union Ministry of Finance plays a crucial role in the financial matters of the country, it does not recommend the principles governing grants-in-aid. Its responsibilities include formulating and implementing the Union Budget, managing public finances, and formulating financial policies.
d) Public Accounts Committee: The Public Accounts Committee is a parliamentary committee that examines the audit reports of the Comptroller and Auditor General (CAG) of India. Its primary role is to scrutinize the government's expenditure and financial transactions. It does not recommend principles governing grants-in-aid.

In conclusion, the Finance Commission is the authority responsible for recommending the principles governing grants-in-aid of the revenues to the states out of the Consolidated Fund of India.