The population of a village increased from 800 to 900. Find the percentage increase.

The population increased from 800 to 900.

$$\text{Increase} = \text{New population} - \text{Original population}$$ $$\text{Increase} = 900 - 800$$ $$\text{Increase} = 100$$

The formula for percentage increase is:

$$\text{Percentage Increase} = \frac{\text{Increase}}{\text{Original population}} \times 100\%$$

Substitute the values:

$$\text{Percentage Increase} = \frac{100}{800} \times 100\%$$

$$\text{Percentage Increase} = \frac{1}{8} \times 100\%$$ $$\text{Percentage Increase} = 0.125 \times 100\%$$ $$\text{Percentage Increase} = 12.5\%$$

The percentage increase is $\boxed{12.5\%}$.