Let's denote the total number of apples Sarah picked as \( x \).
- She discarded \( \frac{1}{10} \) of the apples as defective. Therefore, the number of apples discarded is:
\[ \frac{1}{10} x \]
- The number of apples remaining after discarding the defective ones is:
\[ x - \frac{1}{10} x = \frac{9}{10} x \]
- According to the problem, 300 of the remaining apples were made into cider. This tells us that:
\[ \frac{9}{10} x - 300 \]
represents the number of remaining apples after making cider, which were then sold as fresh fruit.
- The number of apples sold as fresh fruit is thus:
\[ \text{Fresh fruit} = \frac{9}{10} x - 300 \]
- Now, we need to find the fraction of the total apples picked that were sold as fresh fruit. This fraction can be expressed as:
\[ \frac{\text{Fresh fruit}}{x} = \frac{\frac{9}{10} x - 300}{x} \]
We can simplify this fraction:
\[ \frac{\frac{9}{10} x - 300}{x} = \frac{9}{10} - \frac{300}{x} \]
Now, we want to determine the amount of \( x \) such that the number of apples sold as fresh fruit makes sense. We set up the equation for fresh fruit:
\[ \frac{9}{10} x - 300 > 0 \]
This means that:
\[ \frac{9}{10} x > 300 \]
Multiplying both sides by \( \frac{10}{9} \):
\[ x > \frac{300 \times 10}{9} = \frac{3000}{9} \approx 333.33 \]
For the sake of simplicity, let's assume \( x = 400 \), to test. Then:
- The apples discarded are:
\[ \frac{1}{10} \times 400 = 40 \]
- The apples remaining would be:
\[ 400 - 40 = 360 \]
- The number of apples made into cider is 300, so the number of apples sold as fresh fruit would be:
\[ 360 - 300 = 60 \]
Now we calculate the fraction of total apples that were sold as fresh fruit:
\[ \frac{60}{400} = \frac{3}{20} \]
Now, validating \( x = 400 \) against the earlier constraints shows it meets the requirement, as \( x > 333.33 \).
Thus, the fraction of total apples picked that were sold as fresh fruit is:
\[ \boxed{\frac{3}{20}} \]