CA Foundation · Quantitative Aptitude · Index Numbers
An old index series (base 2008 = 100) stood at 200 in 2016 and was then discontinued. A new series (base 2016 = 100) shows 130 for 2020. Splicing the new series to the old base, what is the index for 2020 on base 2008 = 100?
The spliced index for 2020 is 260. The new series value of 130 is multiplied by the old series value of 200 at the linking year 2016 and divided by 100, which carries the 30% rise onto the old base.
- A330
- B65
- C230
- D260Correct
Explanation
Spliced index = new index × old index of the linking year / 100 = 130 × 200/100 = 260. Check: 200 grew by 30% to 260. Adding the two values (330) is wrong because the series are linked by ratio, not by sum. Dividing 130 by 200 × 100 gives 65, which inverts the factor.
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