From `1980-1990`, the population of a country was increased by `20%`.
From `1990-2000`, the population of the country was increased by `20%`.
From `2000-2010`, the population of the country was increased by `20%`.
Then the overall increased population (in percentage) of the country from `1980-2010` was.

Options

A. a) `60%`
B. b) `62.8%`
C. c) `72.2%`
D. d) `72.8%`

Answer

To find the overall percentage increase in the population of a country from 1980 to 2010, given that the population increased by 20% during each decade, we can follow these steps:

### Step 1: Assume Initial Population
Let the initial population in 1980 be \( P = 100 \).

### Step 2: Calculate Population after 1990
From 1980 to 1990, the population increased by 20%.
- Increase = \( 20\% \) of \( 100 = \frac{20}{100} \times 100 = 20 \)
- Population in 1990 = \( 100 + 20 = 120 \)

### Step 3: Calculate Population after 2000
From 1990 to 2000, the population again increased by 20%.
- Increase = \( 20\% \) of \( 120 = \frac{20}{100} \times 120 = 24 \)
- Population in 2000 = \( 120 + 24 = 144 \)

### Step 4: Calculate Population after 2010
From 2000 to 2010, the population increased by 20% once more.
- Increase = \( 20\% \) of \( 144 = \frac{20}{100} \times 144 = 28.8 \)
- Population in 2010 = \( 144 + 28.8 = 172.8 \)

### Step 5: Calculate Overall Percentage Increase
Now, we need to find the overall percentage increase from 1980 to 2010.
- Overall increase = Final population - Initial population = \( 172.8 - 100 = 72.8 \)
- Percentage increase = \( \left( \frac{72.8}{100} \right) \times 100 = 72.8\% \)

### Final Answer
The overall percentage increase in the population from 1980 to 2010 is **72.8%**.

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