The price index of a commodity is 99. What does it indicate about the charge in price of the commodity in current year as compared to base year?

Answer

To solve the question regarding the price index of a commodity being 99, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Price Index**:
The price index (PI) is a measure that compares the current price of a commodity to its price in a base year. It is calculated using the formula:
\[ PI = \left( \frac{P_c}{P_b} \right) \times 100 \]
where \( P_c \) is the current price and \( P_b \) is the base price.

2. **Setting Up the Equation**:
Given that the price index is 99, we can set up the equation:
\[ 99 = \left( \frac{P_c}{P_b} \right) \times 100 \]

3. **Rearranging the Equation**:
To find the ratio of the current price to the base price, we can rearrange the equation:
\[ \frac{P_c}{P_b} = \frac{99}{100} \]

4. **Interpreting the Ratio**:
The ratio \( \frac{P_c}{P_b} = 0.99 \) indicates that the current price is 99% of the base price. This means that if the base price ( \( P_b \) ) is considered to be 100, then the current price ( \( P_c \) ) is:
\[ P_c = 0.99 \times P_b \]
If we assume \( P_b = 100 \), then:
\[ P_c = 0.99 \times 100 = 99 \]

5. **Conclusion**:
Since the current price (99) is less than the base price (100), this indicates that there has been a decrease in the price of the commodity compared to the base year. Specifically, the price has decreased by 1%.

### Final Answer:
The price index of 99 indicates that the price of the commodity has decreased by 1% in the current year compared to the base year.

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