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The price of 5 items for the year 2004 2,5/2,3,9/4and 18/5 items the prices of the same items for the base year 1995.if a family on an average spends 40%,30%,10%,15%and 5% of it income responsibility on these items find the common index numbers for these items?
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The price of 5 items for the year 2004 2,5/2,3,9/4and 18/5 items the p...
Common Index Numbers for Items


Introduction


This question is about calculating the common index numbers for five items based on their prices in the year 2004 and the base year 1995. The items are responsible for 40%, 30%, 10%, 15%, and 5% of a family's income, respectively.


Calculating Price Relative


The first step in calculating the common index numbers is to find the price relative for each item. Price relative is the ratio of the price of an item in the current year to its price in the base year.



  • Item 1: Price relative = (2.5 / 1.5) x 100 = 166.67

  • Item 2: Price relative = (2.3 / 1.5) x 100 = 153.33

  • Item 3: Price relative = (9 / 5) x 100 = 180

  • Item 4: Price relative = (4 / 3) x 100 = 133.33

  • Item 5: Price relative = (18 / 10) x 100 = 180



Calculating Weighted Aggregate of Price Relative


The next step is to calculate the weighted aggregate of the price relative for each item. Weighted aggregate is the product of the price relative and the weight of each item.



  • Item 1: Weighted aggregate = 166.67 x 0.4 = 66.67

  • Item 2: Weighted aggregate = 153.33 x 0.3 = 46

  • Item 3: Weighted aggregate = 180 x 0.1 = 18

  • Item 4: Weighted aggregate = 133.33 x 0.15 = 19.99

  • Item 5: Weighted aggregate = 180 x 0.05 = 9



Calculating the Common Index Numbers


The last step is to calculate the common index numbers by dividing the sum of the weighted aggregates by the sum of the weights.


Common Index Number = Sum of Weighted Aggregates / Sum of Weights


Common Index Number = (66.67 + 46 + 18 + 19.99 + 9) / (0.4 + 0.3 + 0.1 + 0.15 + 0.05) = 44.58


Conclusion


The common index number for the five items is 44.58. This means that the prices of the five items have increased by 44.58% since the base year 1995. The calculation of common index numbers is essential for analyzing the changes in prices over time and making informed decisions based on the inflation rate.
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The price of 5 items for the year 2004 2,5/2,3,9/4and 18/5 items the prices of the same items for the base year 1995.if a family on an average spends 40%,30%,10%,15%and 5% of it income responsibility on these items find the common index numbers for these items?
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