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%