Introduction:
In order to calculate the weighted price index number, we need to consider the relative importance of each commodity and the percentage change in their prices. The relative importance is given as a ratio of 3:3:1 for the three commodities.

Calculating the weighted price index number:
To calculate the weighted price index number, we need to follow these steps:

Step 1: Calculate the price change for each commodity:
- The price of the first commodity increased by 10%. Let's assume the initial price of this commodity was P1. Therefore, the new price would be P1 + 10% of P1, which can be written as P1 + 0.1P1.
- The price of the second commodity increased by 20%. Let's assume the initial price of this commodity was P2. Therefore, the new price would be P2 + 20% of P2, which can be written as P2 + 0.2P2.
- The price of the third commodity decreased by 30%. Let's assume the initial price of this commodity was P3. Therefore, the new price would be P3 - 30% of P3, which can be written as P3 - 0.3P3.

Step 2: Calculate the weighted price change for each commodity:
- Multiply the price change for each commodity by its relative importance ratio. For the first two commodities, the relative importance is 3, and for the third commodity, it is 1.
- The weighted price change for the first commodity would be 3 times the price change of the first commodity, which is 3 * (P1 + 0.1P1).
- The weighted price change for the second commodity would be 3 times the price change of the second commodity, which is 3 * (P2 + 0.2P2).
- The weighted price change for the third commodity would be 1 times the price change of the third commodity, which is 1 * (P3 - 0.3P3).

Step 3: Calculate the weighted average price change:
- Add up the weighted price changes for all three commodities.
- The weighted average price change would be the sum of the weighted price changes divided by the sum of the relative importance ratios (3 + 3 + 1).
- Let's assume the sum of the weighted price changes is W.
- The weighted average price change can be calculated as W / 7.

Step 4: Calculate the weighted price index number:
- The weighted price index number is obtained by adding 100 to the weighted average price change.
- The formula to calculate the weighted price index number is (W / 7) + 100.

Explanation:
The above steps outline the process of calculating the weighted price index number based on the given information. By following these steps, we can determine the change in the overall price level, taking into account the relative importance of each commodity. This allows for a more accurate representation of price changes and their impact on the overall economy.