Q.The Consumer Price Index (CPI) of a country stood at 200 in the year 2023 and rose to 220 in the year 2024. Calculate the rate of inflation for the year 2024.

The inflation rate compares the change in the price index to its earlier value, expressed as a percentage — a direct application of the standard inflation-rate formula.

Step 1 — Apply the formula. $\text{Inflation Rate (\%)} = \dfrac{\text{Price Index}_{\text{current}} - \text{Price Index}_{\text{previous}}}{\text{Price Index}_{\text{previous}}} \times 100$

Step 2 — Substitute the values. Current-year (2024) CPI = 220; previous-year (2023) CPI = 200.

$\text{Inflation Rate} = \dfrac{220-200}{200}\times100 = \dfrac{20}{200}\times100 = 10\%$

Step 3 — Cross-check (dual solve). Expressed as a ratio, the 2024 index is $220/200 = 1.10$ times the 2023 index — i.e. exactly 10% higher, which matches the formula's result and confirms the arithmetic.

As a quick cross-check on any inflation-rate numerical, compute the ratio of the two index values directly (current ÷ previous); the amount by which that ratio exceeds 1, expressed as a percentage, must equal the answer from the standard formula.

A common slip is dividing the price change by the current year's index instead of the previous (base) year's index — the formula always divides by the earlier/previous period's value, since the inflation rate measures the rise relative to where prices started, not where they ended.