10 questions · Form 4 Additional Mathematics Bab 10: Index Numbers
The price index of petrol was 120 in 2022 based on 2018, and 150 in 2024 based on 2018. Find the price index of petrol in 2024 based on 2022.
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. The price index of petrol was 120 in 2022 based on 2018, and 150 in 2024 based on 2018. Find the price index of petrol in 2024 based on 2022.
Answer: A
I₂₀₂₄/₂₀₂₂ = (I₂₀₂₄/₂₀₁₈ / I₂₀₂₂/₂₀₁₈) × 100 = (150120) × 100 = 1.25 × 100 = 125.
2. The prices of a bicycle in 2018 and 2022 were RM 400 and RM 520 respectively. Find the price index for 2022 based on 2018.
Answer: A
I = (520400) × 100 = 1.3 × 100 = 130.
3. The price index of an item in 2023 based on 2021 is 135. If the price in 2021 was RM 80, what was its price in 2023?
Answer: A
I = (Q₁ / Q₀) × 100 => 135 = (Q₂₀₂₃ / 80) × 100 => Q₂₀₂₃ = 135 × 80100 = RM 108.
4. The price index of a shirt in 2022 based on 2020 is 125, and the price index in 2024 based on 2022 is 110. Calculate the price index in 2024 based on 2020.
Answer: A
I₂₀₂₄/₂₀₂₀ = (I₂₀₂₂/₂₀₂₀ × I₂₀₂₄/₂₀₂₂) / 100 = 125 × 110100 = 13750100 = 137.5.
5. Three items have price indices of 110, 125, and x with weightages of 3, 2, and 5 respectively. If the composite index is 120, find the value of x.
Answer: A
Ī = 110(3) + 125(2) + 5x3 + 2 + 5 => 120 = 330 + 250 + 5x10 => 1200 = 580 + 5x => 5x = 620 => x = 124.
6. A production index consists of two parts with weightages 60% and 40%. If their indices are 110 and 130 respectively, what is the composite index?
Answer: A
Ī = 110 × 60 + 130 × 40100 = 6600 + 5200100 = 11800100 = 118.
7. If all components in a composite index increase by 10%, what happens to the composite index?
Answer: A
If every component index I_i becomes 1.10 × I_i, the composite index becomes Σ(1.10 I_i w_i) / Σw_i = 1.10 × Ī, which represents a 10% increase.
8. In a pie chart representing weightages, component X occupies an angle of 90°. What is the weightage of component X as a fraction of the total?
Answer: A
Weightage fraction = 90° / 360° = 14.
9. If the price index of a good in 2024 based on 2020 is 140, what is the percentage increase in price from 2020 to 2024?
Answer: A
Percentage increase = I - 100 = 140 - 100 = 40%.
10. If the price index of electricity in 2024 based on 2020 is 100, this means:
Answer: A
An index of 100 indicates zero change in price relative to the base year.