CA Foundation · Quantitative Aptitude · Index Numbers
A CPI series (base 2015 = 100) shows 200 for 2023. A family's income was ₹30,000 in 2015 and is ₹54,000 in 2023. By what percentage has the family's real income changed relative to 2015?
The family's real income fell by 10%. Deflating the 2023 income of ₹54,000 by the CPI of 200 gives ₹27,000 in base-year prices, which is below the 2015 income of ₹30,000 by ₹3,000, or 10 percent.
- AIncreased by 80%
- BDecreased by 10%Correct
- CIncreased by 10%
- DDecreased by 20%
Explanation
Real income 2023 = 54,000 × 100/200 = ₹27,000. Real income in 2015 = ₹30,000. Change = (27,000 − 30,000)/30,000 = −10%. Option A looks only at money income, ignoring the price rise.
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