Question:
What is the population of State A in 2026?
Statement (I): The population of A in 2020 was three crore and the rate of increase of population is \(2.5\%\) per year.
Statement (II): The population of A in 2026 is twice the population of A in 2020.
What is the population of State A in 2026?
Statement (I): The population of A in 2020 was three crore and the rate of increase of population is \(2.5\%\) per year.
Statement (II): The population of A in 2026 is twice the population of A in 2020.
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Whenever an initial population and annual growth rate are known, compound growth can be used to determine the future population uniquely.
Updated On: Jun 12, 2026
- Statement I alone is sufficient, but Statement II alone is not sufficient.
- Statement II alone is sufficient, but Statement I alone is not sufficient.
- Both statements together are sufficient, but neither statement alone is sufficient.
- Even both statements together are not sufficient.
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The Correct Option is A
Solution and Explanation
Concept:
Population growth generally follows the compound growth formula
\[
P=P_0\left(1+\frac{r}{100}\right)^n,
\]
where
\[
P_0=\text{Initial population},
\]
\[
r=\text{Annual growth rate},
\]
\[
n=\text{Number of years}.
\]
Step 1: Analyze Statement (I). Given: \[ P_0=3 \text{ crore} \] and \[ r=2.5\%. \] The period from 2020 to 2026 is \[ n=6. \] Hence \[ P=3(1.025)^6. \] A unique value can be computed. Therefore Statement (I) alone is sufficient.
Step 2: Analyze Statement (II). Given: Population in 2026 is twice that in 2020. However, the population in 2020 is unknown. Hence \[ P_{2026}=2P_{2020} \] cannot be numerically evaluated. Statement (II) alone is insufficient.
Step 1: Analyze Statement (I). Given: \[ P_0=3 \text{ crore} \] and \[ r=2.5\%. \] The period from 2020 to 2026 is \[ n=6. \] Hence \[ P=3(1.025)^6. \] A unique value can be computed. Therefore Statement (I) alone is sufficient.
Step 2: Analyze Statement (II). Given: Population in 2026 is twice that in 2020. However, the population in 2020 is unknown. Hence \[ P_{2026}=2P_{2020} \] cannot be numerically evaluated. Statement (II) alone is insufficient.
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