Question

The population of a country increased by 5% from 2020 to 2021. Then, the population decreased by 5% from 2021 to 2022. By what percentage did the population change from 2020 to 2022?

• A. -0.25%
• B. 0%
• C. 2.5%
• D. 10.25%

Hint:

Remember that a 5% increase followed by a 5% decrease does not cancel out — it produces a slight net decrease because percentages apply to different bases.

Answer 1

The Correct Option is A

 

Step 1: Assume initial population in 2020.
Let the population in 2020 be \(P = 100\).

Step 2: Population in 2021 after 5% increase.
\[ P_{2021} = 100 \times (1 + 0.05) = 105 \]

Step 3: Population in 2022 after 5% decrease.
\[ P_{2022} = 105 \times (1 - 0.05) = 105 \times 0.95 = 99.75 \]

Step 4: Net percentage change from 2020 to 2022.
\[ %\ \Delta P = \frac{99.75 - 100}{100} \times 100 = -0.25% \] 

\[ \boxed{-0.25\%} \]