To calculate index numbers using Paasche's method and Fisher's method, we first need to understand what these methods entail:

1. Paasche's Method:
   - Paasche's index is a Laspeyres-type index, which means it uses the current period's quantities as weights.
   - The formula for Paasche's Price Index (PPI) is: 

   \[PPI = \frac{\sum_{i=1}^{n} (P_{i}^{c} \cdot Q_{i}^{c})}{\sum_{i=1}^{n} (P_{i}^{b} \cdot Q_{i}^{c})} \times 100\]

   Where:
   - \(P_{i}^{c}\) = Current period's price of commodity i
   - \(P_{i}^{b}\) = Base period's price of commodity i
   - \(Q_{i}^{c}\) = Current period's quantity of commodity i
   - n = Number of commodities

2. Fisher's Method:
   - Fisher's index is a geometric mean of the Paasche and Laspeyres indices.
   - The formula for Fisher's Price Index (FPI) is:

   \[FPI = \sqrt{Paasche \times Laspeyres}\]

   Where:
   - \(Paasche\) = Paasche's Price Index
   - \(Laspeyres\) = Laspeyres Price Index

Now, let's calculate the price indices for the given data using both Paasche's and Fisher's methods:

Step 1: Calculate the Laspeyres Price Index (LPI)

To calculate the Laspeyres index, we need a base period. Let's assume the base period is the first period (i.e., period A). We'll calculate the price indices for all commodities relative to period A.

For commodity A (base period):
- \(P_{A}^{b} = 5\)
- \(Q_{A}^{b} = 14\)

For commodity