To find the difference in height between the two positions of the parasail, we will subtract the lower height from the higher height.
The initial height of the parasail is \( \frac{1}{20} \) of a kilometer, and the subsequent height is \( \frac{1}{50} \) of a kilometer.
First, we need a common denominator to perform the subtraction. The least common multiple (LCM) of 20 and 50 is 100.
Now, we convert both fractions to have the same denominator of 100:
\[ \frac{1}{20} = \frac{5}{100} \quad (\text{since } 1 \div 20 = 0.05, \text{ and } 0.05 \cdot 100 = 5) \]
\[ \frac{1}{50} = \frac{2}{100} \quad (\text{since } 1 \div 50 = 0.02, \text{ and } 0.02 \cdot 100 = 2) \]
Now, we can subtract:
\[ \frac{5}{100} - \frac{2}{100} = \frac{5 - 2}{100} = \frac{3}{100} \]
Therefore, the difference in height is \( \frac{3}{100} \) kilometers.
The answer is:
A. \( \frac{3}{100} \) kilometers.