CA Foundation · Quantitative Aptitude · Index Numbers
A price index series on base 2012 = 100 shows 180 for 2020. A new series with base 2020 = 100 shows 125 for 2024. Splicing the new series onto the old one, what is the 2024 index on base 2012 = 100?
The spliced 2024 index on base 2012 is 225. Multiply the new series value 125 by the old series value for the link year 2020, which is 180, and divide by 100. This chains the two series onto one common base.
- A225Correct
- B205
- C144
- D55.6
Explanation
Spliced value = new index × old index of the link year / 100 = 125 × 180 / 100 = 225. Adding the numbers (180 + 125 = 305 less 100 = 205) is the wrong approach. Dividing 180 by 125 gives 144, which inverts the ratio.
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