Q.Ramesh earns a fixed monthly salary of ₹24,000. In the base year, the Consumer Price Index (CPI) was 100, so his real income equalled his nominal income. Three years later his salary is unchanged at ₹24,000, but the CPI has risen to 150. Calculate his real income in the third year and the percentage fall in his real income.

Because Ramesh's money salary never changes while prices rise, his real (purchasing-power) income falls — exactly the 'fixed-income earners lose' effect of inflation, shown here in numbers.

Step 1 — Apply the real-income formula. $\text{Real Income} = \dfrac{\text{Nominal Income}}{\text{Price Index}} \times 100$

Step 2 — Substitute the values. Nominal income = ₹24,000; current CPI = 150.

$\text{Real Income} = \dfrac{24{,}000}{150}\times100 = ₹16{,}000$

Step 3 — Fall in real income. Base-year real income was ₹24,000 (since base-year CPI = 100 makes real income equal nominal income). The fall is $24{,}000 - 16{,}000 = ₹8{,}000$, which as a percentage of the base-year real income is $\dfrac{8{,}000}{24{,}000}\times100 = 33.33\%$.

Step 4 — Cross-check (dual solve). The ratio of base-year CPI to current CPI is $100/150 = 0.667$; multiplying the nominal income by this ratio gives $24{,}000 \times 0.667 = ₹16{,}000$ — matching Step 2 exactly, confirming the arithmetic.

Cross-check a real-income calculation by multiplying the nominal income directly by the ratio (base-year index ÷ current index) — this must give the identical figure as dividing by the current index and multiplying by 100.

A frequent error is calculating the percentage fall in real income as though it must equal the percentage rise in the price index (here, 50%) — it does not, because real income falls by a smaller proportion than the index rises (33.33% here, against a 50% rise in CPI), since dividing by a larger number is not the same arithmetic operation as the percentage increase in that number.