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Paasche Index

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Paasche Index


1. **State the problem:** Calculate the Paasche quantity index for the basket of items using 2021 as the base year. 2. **Formula:** The Paasche quantity index is given by: $$\text{Paasche Quantity Index} = \frac{\sum (P_1 \times Q_1)}{\sum (P_1 \times Q_0)} \times 100$$ where $P_1$ and $Q_1$ are the prices and quantities in the current year (2024), and $Q_0$ are the quantities in the base year (2021). 3. **Calculate numerator:** Sum of $P_1 \times Q_1$ for 2024: Item 1: $60 \times 70 = 4200$ Item 2: $120 \times 110 = 13200$ Item 3: $170 \times 30 = 5100$ Total numerator = $4200 + 13200 + 5100 = 22500$ 4. **Calculate denominator:** Sum of $P_1 \times Q_0$ using 2024 prices and 2021 quantities: Item 1: $60 \times 40 = 2400$ Item 2: $120 \times 90 = 10800$ Item 3: $170 \times 20 = 3400$ Total denominator = $2400 + 10800 + 3400 = 16600$ 5. **Calculate index:** $$\text{Paasche Quantity Index} = \frac{22500}{16600} \times 100 = 135.54\%$$ 6. **Interpretation:** The Paasche quantity index is approximately 135.5%, which corresponds to option C. **Final answer:** C. 135.5%