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To solve the problem, we need to compute both the price and quantity index in 2003 (using 2001 as the base year) for beans and garri, as well as compute the Aggregate Price Index.

### 1. **Price Index for Beans and Garri**
The price index is computed using the formula:

\[
\text{Price Index} = \left( \frac{\text{Price in 2003}}{\text{Price in 2001}} \right) \times 100
\]

- For **Beans**:
\[
\text{Price Index for Beans} = \left( \frac{5000}{3000} \right) \times 100 = 166.67
\]

- For **Garri**:
\[
\text{Price Index for Garri} = \left( \frac{3000}{1000} \right) \times 100 = 300
\]

### 2. **Quantity Index for Beans and Garri**
The quantity index is computed using the same formula but using the quantity dataTo solve the problem, we need to compute both the price and quantity index in 2003 (using 2001 as the base year) for beans and garri, as well as compute the Aggregate Price Index.

### 1. **Price Index for Beans and Garri**
The price index is computed using the formula:

\[
\text{Price Index} = \left( \frac{\text{Price in 2003}}{\text{Price in 2001}} \right) \times 100
\]

- For **Beans**:
\[
\text{Price Index for Beans} = \left( \frac{5000}{3000} \right) \times 100 = 166.67
\]

- For **Garri**:
\[
\text{Price Index for Garri} = \left( \frac{3000}{1000} \right) \times 100 = 300
\]

### 2. **Quantity Index for Beans and Garri**
The quantity index is computed using the same formula but using the quantity 

\[
\text{Quantity Index} = \left( \frac{\text{Quantity in 2003}}{\text{Quantity in 2001}} \right) \times 100
\]

- For **Beans**:
\[
\text{Quantity Index for Beans} = \left( \frac{4}{2} \right) \times 100 = 200
\]

- For **Garri**:
\[
\text{Quantity Index for Garri} = \left( \frac{6}{3} \right) \times 100 = 200
\]

### 3. **Aggregate Price Index**
The Aggregate Price Index is calculated as a weighted price index, where the quantities in the base year are used as weights:

\[
\text{Aggregate Price Index} = \frac{(P_1 \times Q_0) + (P_2 \times Q_0)}{(P_0 \times Q_0) + (P_0 \times Q_0)} \times 100
\]
Where:
- \( P_1 \) and \( P_2 \) are prices in 2003 for beans and garri.
- \( P_0 \) is the price in 2001.
- \( Q_0 \) is the quantity in 2001.

Let's now compute it.

For beans and garri:
- Beans price in 2003: 5000, price in 2001: 3000, quantity in 2001: 2
- Garri price in 2003: 3000, price in 2001: 1000, quantity in 2001: 3

\[
\text{Aggregate Price Index} = \frac{(5000 \times 2) + (3000 \times 3)}{(3000 \times 2) + (1000 \times 3)} \times 100
\]

Let me calculate the value now.The Aggregate Price Index is approximately **211.11**.

### Summary:
1. **Price Index for Beans**: 166.67
2. **Price Index for Garri**: 300
3. **Quantity Index for Beans**: 200
4. **Quantity Index for Garri**: 200
5. **Aggregate Price Index**: 211.11

Would you like further details or explanations?

Here are 5 related questions:
1. How does the price index help in understanding inflation?
2. What is the significance of using the base year in such computations?
3. How would changing the base year affect the price index?
4. What are other methods of calculating aggregate price indices?
5. How can we incorporate more items into the aggregate price index?

**Tip**: The price index can be used to track changes in the cost of living or inflation rates over time.

The table below shows the prices and quantity demanded of some basic food items in 2001 and 2003. Using 2001 as the base year, compute the price and quantity index in 2003 for beans and garri, and compute the Aggregate Price Index.

This page provides a detailed solution for calculating price and quantity indices for beans and garri in 2003 using 2001 as the base year. It also includes a calculation of the aggregate price index using weighted averages, suitable for college-level economics or statistics courses.

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