CA Foundation · Quantitative Aptitude · Index Numbers
A price index series with base 2015 = 100 reads 2018: 120, 2020: 150, 2023: 210. If the base is shifted to 2020 = 100, what is the percentage rise in prices from 2018 to 2023 as shown by the shifted series?
Prices rose by 75%. On the shifted base 2020 = 100, the 2018 index is 80 and the 2023 index is 140. The rise is 60 on a base of 80, giving 75%. Base shifting does not alter the percentage change between two years.
- A75%Correct
- B40%
- C60%
- D85%
Explanation
Shifted index for 2018 = 120/150 × 100 = 80. Shifted index for 2023 = 210/150 × 100 = 140. Rise = (140 − 80)/80 × 100 = 75%. Using 210 − 150 = 60 or 140 − 100 = 40 uses the wrong base; the rate of change is the same on either base: (210 − 120)/120 = 75%.
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