10 questions · Form 4 Additional Mathematics Bab 10: Index Numbers
The price of a laptop in the year 2020 was RM 2,500. In 2024, its price increased to RM 3,000. Calculate the price index of the laptop in 2024 based on the year 2020.
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. The price of a laptop in the year 2020 was RM 2,500. In 2024, its price increased to RM 3,000. Calculate the price index of the laptop in 2024 based on the year 2020.
Answer: A
Price Index I = (Q₁ / Q₀) × 100 = (30002500) × 100 = 1.2 × 100 = 120.
2. 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%.
3. A price index of 85 indicates that the price of an item has:
Answer: A
Since 85 is less than 100, the price decreased by (100 - 85)% = 15% compared to the base year.
4. If the price of raw material increases by 20% from 2021 to 2023, what is its price index in 2023 based on 2021?
Answer: A
A 20% increase means the price index is 100 + 20 = 120.
5. In a bakery, flour, sugar, and butter are used in the ratio 5 : 2 : 3. These ratios represent the:
Answer: A
Ratios of components used in production represent their relative importance or weightage (w_i).
6. The composite index for manufacturing a handbag in 2023 based on 2020 is 128. If the cost of manufacturing the handbag in 2020 was RM 75, find the manufacturing cost in 2023.
Answer: A
Cost in 2023 = Composite Index × Cost in 2020100 = 128 × 75100 = 9600100 = RM 96.
7. The prices of a commodity in 2019 and 2023 are RM 15.00 and RM 18.75 respectively. Calculate the price index in 2023 based on 2019.
Answer: A
I = (18.7515.00) × 100 = 1.25 × 100 = 125.
8. Four components A, B, C, and D have price indices 110, 120, 130, and 100 with weightages 2, 3, 4, and 1 respectively. Calculate the composite index.
Answer: A
Composite Index Ī = Σ(I_i × w_i) / Σw_i = 110(2) + 120(3) + 130(4) + 100(1)2 + 3 + 4 + 1 = 220 + 360 + 520 + 10010 = 120010 = 120. Wait, let us compute accurately: 220 + 360 + 520 + 100 = 120010 = 120. Let us adjust calculation: 110(2)=220, 120(3)=360, 130(4)=520, 100(1)=100. Total = 1200. Div by 10 = 120.
9. 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.
10. 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.