Quantity Index Number by Weighted Aggregate Method is given by ................ .

Answer

To find the Quantity Index Number by the Weighted Aggregate Method, we follow these steps:

### Step-by-Step Solution:

1. **Define the Variables**:
- Let \( Q_0 \) be the quantity of the base year.
- Let \( Q_1 \) be the quantity of the current year.
- Let \( W \) be the weight of each commodity.

2. **Calculate the Weighted Quantity for the Current Year**:
- The weighted quantity for the current year is calculated as:
\[ \text{Weighted Quantity for Current Year} = \sum (Q_1 \times W) \]
- This means we multiply the quantity of each commodity in the current year by its corresponding weight and then sum these products.

3. **Calculate the Weighted Quantity for the Base Year**:
- The weighted quantity for the base year is calculated as:
\[ \text{Weighted Quantity for Base Year} = \sum (Q_0 \times W) \]
- Similarly, we multiply the quantity of each commodity in the base year by its corresponding weight and sum these products.

4. **Calculate the Quantity Index Number**:
- The Quantity Index Number (QIN) is given by the formula:
\[ QIN = \frac{\sum (Q_1 \times W)}{\sum (Q_0 \times W)} \times 100 \]
- This formula gives us the index number by taking the ratio of the weighted quantity for the current year to the weighted quantity for the base year, multiplied by 100.

5. **Interpret the Result**:
- The result indicates how the quantity of commodities has changed from the base year to the current year in relation to their weights.

### Final Answer:
The Quantity Index Number by the Weighted Aggregate Method is given by:
\[ QIN = \frac{\sum (Q_1 \times W)}{\sum (Q_0 \times W)} \times 100 \]

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