Question

Calculate price index number from the following data: 

 \[ \begin{array}{|c|c|c|c|c|} \hline \text{Commodity} & A & B & C & D \\ \hline \text{Price in 2005 (₹)} & 6 & 16 & 24 & 4 \\ \hline \text{Price in 2010 (₹)} & 8 & 18 & 28 & 6 \\ \hline \end{array} \]

Hint:

The Price Index number is a measure of the relative change in prices between two time periods.

Answer 1

Step 1: Formula for Price Index Number.
The formula for calculating the Price Index number is: \[ \text{Price Index} = \frac{\text{Price in 2010}}{\text{Price in 2005}} \times 100 \]

Step 2: Calculate for each commodity.
For Commodity A: \[ \text{Price Index for A} = \frac{8}{6} \times 100 = 133.33 \] For Commodity B: \[ \text{Price Index for B} = \frac{18}{16} \times 100 = 112.50 \] For Commodity C: \[ \text{Price Index for C} = \frac{28}{24} \times 100 = 116.67 \] For Commodity D: \[ \text{Price Index for D} = \frac{6}{4} \times 100 = 150.00 \]

Step 3: Conclude.
The Price Index numbers for the commodities are: \[ \boxed{A = 133.33, B = 112.50, C = 116.67, D = 150.00} \]