CA Foundation · Quantitative Aptitude · Index Numbers
In 2015 a wholesale price index (base 2005 = 100) read 250. The series was then discontinued and a new series with base 2015 = 100 began. In 2020 the new series read 120. Using splicing, what is the 2020 value on the old base 2005 = 100?
The 2020 value on base 2005 is 300. Splicing links the new series to the old by multiplying the new index of 120 by the old 2015 index of 250 divided by 100. Index values are multiplicative ratios, so they cannot simply be added.
- A300Correct
- B370
- C208
- D270
Explanation
Splice by multiplying the new index by old index at the link year divided by 100: 120 × 250/100 = 300. Adding the values gives 370, which is wrong because indices are ratios and not additive. Dividing gives 120 × 100/250 = 48 in the other direction, and 208 comes from 250 × 100/120, also wrong.
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