Let's break down the problem:

1. Selling 80%: The vendor sells 80% of the fruits. This means that 20% of the fruits are left.

2. Throwing Away 10% of Remaining Fruits: The vendor then discards 10% of the remaining 20%.

   $10\% \text{ of } 20\% = 0.1 \times 20 = 2\%$

So, the total percentage of discarded fruits in relation to the original total is 2%.

Answer: 2%

Would you like further details or explanations?

Here are some related questions for practice:

1. If a vendor sells 70% of the fruits and discards 20% of the remaining, what is the total discarded percentage?
2. How would the answer change if the vendor sells 85% and discards 5% of the remaining?
3. What if the vendor initially keeps 50% and discards 10% of what’s left?
4. Suppose the vendor discards a different percentage of the remaining stock, say 15%. What would be the outcome?
5. How can the formula be generalized if different percentages are sold and discarded?

Tip: When dealing with percentages of remaining quantities, calculate each step sequentially to ensure accuracy.