Factor Reversal Test:
The factor reversal test is a test used to determine whether an index satisfies the factor reversal property. The factor reversal property states that if two price indices are calculated using the same set of prices but with the quantities of different periods, the two indices should be reciprocals of each other.

Fishers Ideal Index:
The Fishers Ideal Index is a method used to calculate price indices. It is based on the geometric mean of the Laspeyres and Paasche indices. The Laspeyres index uses the quantities of a base period and the prices of the current period, while the Paasche index uses the quantities of the current period and the prices of the current period.

Laspeyres Index:
The Laspeyres index is a method used to calculate price indices. It compares the cost of purchasing a fixed basket of goods and services in different periods. The quantities used in the index calculation are from a base period, while the prices used are from the current period.

Paasches Index:
The Paasches index is another method used to calculate price indices. It also compares the cost of purchasing a fixed basket of goods and services in different periods. However, the quantities used in the index calculation are from the current period, while the prices used are from the current period as well.

Explanation:
The factor reversal test states that if two price indices are calculated using the same set of prices but with the quantities of different periods, the two indices should be reciprocals of each other. In other words, if we calculate the index using the quantities of the base period and the prices of the current period, and then calculate the index using the quantities of the current period and the prices of the current period, the two indices should be reciprocals.

The Fishers Ideal Index satisfies the factor reversal test because it is based on the geometric mean of the Laspeyres and Paasche indices. The Laspeyres index uses the quantities of the base period and the prices of the current period, while the Paasche index uses the quantities of the current period and the prices of the current period. Therefore, when calculating the Fishers Ideal Index, the quantities used in the index calculation are from different periods, satisfying the factor reversal test.

On the other hand, the Laspeyres and Paasche indices do not satisfy the factor reversal test individually. The Laspeyres index uses the quantities of the base period and the prices of the current period, while the Paasche index uses the quantities and prices of the current period. Therefore, when calculating these indices, the quantities used in the index calculation are from the same period, not satisfying the factor reversal test.

In conclusion, the correct answer is option 'A' - Fishers Ideal Index, as it is the only index among the given options that satisfies the factor reversal test.