`(sump_1q_1w)/(sump_0q_0w)xx100` gives

Options

A. Value Index Number by Simple Aggregate method
B. Value Index Number by Weighted Aggregate method
C. Cost of Living Index Number
D. Laspeyre’s Index Number

Answer

To solve the expression \((\text{sump}_1q_1w)/(\text{sump}_0q_0w) \times 100\), we need to understand the components involved in the formula.

### Step-by-Step Solution:

1. **Identify the Components**:
- Let \( P_1 \) be the current price of the commodity.
- Let \( Q_1 \) be the current quantity of the commodity.
- Let \( P_0 \) be the base price of the commodity.
- Let \( Q_0 \) be the base quantity of the commodity.
- Let \( W \) be the respective weights of the commodities.

2. **Calculate the Current Value**:
- The current value can be represented as:
\[ \text{sump}_1q_1w = \sum (P_1 \cdot Q_1 \cdot W) \]
- This represents the total value of the commodities at current prices and quantities, weighted by their respective weights.

3. **Calculate the Base Value**:
- The base value can be represented as:
\[ \text{sump}_0q_0w = \sum (P_0 \cdot Q_0 \cdot W) \]
- This represents the total value of the commodities at base prices and quantities, also weighted.

4. **Formulate the Index Number**:
- The formula for the index number is given by:
\[ \text{Index Number} = \left( \frac{\text{sump}_1q_1w}{\text{sump}_0q_0w} \right) \times 100 \]
- This formula compares the current weighted value to the base weighted value and expresses it as a percentage.

5. **Interpret the Result**:
- The result of this calculation gives us a weighted index number, which indicates how much the value of the commodities has changed from the base period to the current period.

### Final Answer:
The expression \((\text{sump}_1q_1w)/(\text{sump}_0q_0w) \times 100\) gives us a weighted index number that reflects the change in value of the commodities from the base period to the current period.