Worksheet Chapter 10: Index Numbers

1. The table below shows the prices and price indices for three ingredients used in making cakes. | Ingredient | Price in 2021 (RM) | Price in 2024 (RM) | Price Index in 2024 (2021=100) | | :--- | :--- | :--- | :--- | | Flour | 2.50 | 3.00 | x | | Sugar | y | 3.50 | 140 | | Butter | 8.00 | z | 125 | Find the values of x, y, and z.

2. A monthly household budget consists of Food, Housing, Utilities, and Transport with weightages in the ratio 4 : 3 : 1 : 2. From 2020 to 2024, the price of Food increased by 25%, Housing increased by 10%, Utilities decreased by 5%, and Transport increased by 15%. (a) Write down the price index for each expenditure category in 2024 based on 2020. (b) Calculate the composite cost of living index for the household in 2024 based on 2020.

3. The pie chart below represents the weightages of four items P, Q, R, and S used in manufacturing an electronic device. Item P has a sector angle of 120°, Item Q has 90°, Item R has 60°, and Item S occupies the remainder. (a) Find the sector angle for Item S. (b) Given the price indices of P, Q, R, and S in 2023 based on 2021 are 110, 125, 140, and 105 respectively, calculate the composite index for the electronic device in 2023 based on 2021.

4. The price of a wooden chair in 2020 was RM 80 and its price in 2023 was RM 104. (a) Calculate the price index of the chair in 2023 based on the year 2020. (b) Interpret the value obtained in (a).

5. True or False: If the price index of an item in 2024 based on 2020 is 120, it means the item costs RM 120 in 2024.

6. The price index of a brand of shoes in 2022 based on 2018 is 120. The price index of the same shoes in 2024 based on 2022 is 115. (a) Calculate the price index of the shoes in 2024 based on 2018. (b) If the price of the shoes was RM 180 in 2018, calculate its price in 2024.

7. The table below shows information about four materials used in making a school uniform. | Material | Price Index (2022 based on 2020) | Change in Index from 2022 to 2024 | Weightage | | :--- | :--- | :--- | :--- | | Fabric | 120 | Increases by 10% | 5 | | Buttons | 110 | Unchanged | 1 | | Thread | 105 | Increases by 5% | 2 | | Zipper | 130 | Decreases by 10% | 2 | (a) Calculate the price index of each material in 2024 based on 2020. (b) Calculate the composite index for making the uniform in 2024 based on 2020. (c) If the cost to make a uniform in 2020 was RM 40, find the cost in 2024.

8. The price index of a bicycle in 2023 based on 2019 is 125. The price index of the bicycle in 2023 based on 2021 is 110. (a) Calculate the price index of the bicycle in 2021 based on 2019. (b) If the bicycle cost RM 550 in 2021, calculate its price in 2019.

9. The table below shows the price indices and weightages for four food items A, B, C, and D used by a restaurant. | Item | Price Index 2022 (2018=100) | Price Index 2024 (2018=100) | Weightage | | :--- | :--- | :--- | :--- | | A | 120 | 135 | 4 | | B | 115 | x | 3 | | C | 140 | 150 | 1 | | D | 110 | 120 | 2 | (a) The composite index for the items in 2022 based on 2018 is 118.5. Calculate the value of item B's index in 2022 if the table above shows 115 (verify if consistent or find missing parameter). (b) Given that the price of item B increases by 20% from 2022 to 2024, find the value of x (Price Index of B in 2024 based on 2018). (c) Calculate the composite index of the restaurant's food items in 2024 based on 2018. (d) The restaurant's total expenditure on these items was RM 12,000 in 2018. Calculate the expected expenditure in 2024.

10. The table below shows the price indices and weightages of four components A, B, C, and D in 2023 based on 2020. | Component | Price Index (2020=100) | Weightage | | :--- | :--- | :--- | | A | 115 | 3 | | B | 130 | 2 | | C | 105 | m | | D | 120 | 1 | Given that the composite index for these four components in 2023 based on 2020 is 115.5, find the value of m.