Price Index Number by using Weighted Aggregate Method is given by

Options

A. `(sump_1q)/(sump_0q)xx100`
B. `sump_1 wxx100`
C. `(sump_1w)/(sump_ow)xx100`
D. `(sump_0w)/(sump_1w)xx100`

Answer

To find the Price Index Number using the Weighted Aggregate Method, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables**:
- Let \( P_0 \) be the base price of the items.
- Let \( P_1 \) be the current price of the items.
- Let \( W \) be the respective weights of the items.

2. **Calculate the Weighted Current Price**:
- The weighted current price is calculated by summing the product of each current price \( P_1 \) and its respective weight \( W \):
\[ \text{Weighted Current Price} = \sum (P_1 \times W) \]

3. **Calculate the Weighted Base Price**:
- Similarly, the weighted base price is calculated by summing the product of each base price \( P_0 \) and its respective weight \( W \):
\[ \text{Weighted Base Price} = \sum (P_0 \times W) \]

4. **Calculate the Price Index Number**:
- The Price Index Number (PIN) is then calculated using the formula:
\[ \text{PIN} = \left( \frac{\sum (P_1 \times W)}{\sum (P_0 \times W)} \right) \times 100 \]

5. **Interpret the Result**:
- The resulting Price Index Number gives an indication of the relative price level of the current prices compared to the base prices, expressed as a percentage.

### Final Formula:
The final formula for the Price Index Number using the Weighted Aggregate Method is:
\[ \text{PIN} = \left( \frac{\sum (P_1 \times W)}{\sum (P_0 \times W)} \right) \times 100 \]