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Let's break down the problem and solve it step-by-step.

### Given Information:
1. **Defeated candidate secured 42% of the valid votes** and lost by 7,68,400 votes.
2. **82,560 votes were declared invalid**.
3. **20% of people did NOT cast their vote**.
4. The question asks for the **percentage of invalid votes** compared to the votes that people **did not cast**, rounded off to 1 decimal place.

### Step-by-step Solution:

1. **Let the total number of eligible voters be \( x \)**.
   - 20% of the total voters did not cast their vote, so:
   \[
   \text{Votes not cast} = 0.2 \times x
   \]

2. **Votes cast**: Since 20% did not vote, the votes cast would be:
   \[
   \text{Votes cast} = 0.8 \times x
   \]

3. **Invalid votes**: We know that 82,560 votes were declared invalid, so:
   \[
   \text{Invalid votes} = 82,560
   \]

4. **Calculate the percentage of invalid votes out of the votes not cast**:
   The percentage is given by:
   \[
   \text{Percentage of invalid votes} = \left( \frac{\text{Invalid votes}}{\text{Votes not cast}} \right) \times 100
   = \left( \frac{82,560}{0.2 \times x} \right) \times 100
   \]

5. **Now calculate \( x \)** (total voters):
   The defeated candidate received 42% of the valid votes and lost by 7,68,400 votes. Therefore, the winning candidate must have received 58% of the valid votes.

   Let the total number of **valid votes** be \( y \). The difference between the votes of the two candidates is:
   \[
   0.58y - 0.42y = 7,68,400
   \]
   Simplifying:
   \[
   0.16y = 7,68,400
   \]
   \[
   y = \frac{7,68,400}{0.16} = 48,02,500
   \]

   So, the total number of valid votes is \( y = 48,02,500 \).

6. **Total votes cast**: 
   Since valid votes exclude invalid votes, the total votes cast is:
   \[
   \text{Votes cast} = 48,02,500 + 82,560 = 48,85,060
   \]

7. **Calculate total voters**:
   The total number of votes cast is 80% of the total number of voters, so:
   \[
   0.8x = 48,85,060
   \]
   Solving for \( x \):
   \[
   x = \frac{48,85,060}{0.8} = 61,06,325
   \]

8. **Calculate votes not cast**:
   \[
   \text{Votes not cast} = 0.2 \times 61,06,325 = 12,21,265
   \]

9. **Final Calculation**:
   Now, the percentage of invalid votes out of the votes not cast is:
   \[
   \text{Percentage of invalid votes} = \left( \frac{82,560}{12,21,265} \right) \times 100 = 6.76\%
   \]

### Answer: 
The invalid votes were **6.8%** (rounded to 1 decimal place) of the votes that were not cast.

---

Would you like further clarification or details on any step? Here are 5 related questions you might be interested in:

1. How do we calculate the total number of votes cast in an election with a mix of valid and invalid votes?
2. How do invalid votes affect the overall election result in terms of percentages?
3. Can you explain the difference between valid votes, invalid votes, and votes not cast?
4. How does a margin of defeat relate to calculating the total number of voters?
5. How would changing the percentage of invalid votes affect the final outcome?

**Tip**: When solving election problems, always distinguish between the total number of voters, votes cast, valid votes, and invalid votes to avoid confusion.

In an election between two candidates, the defeated candidate secured 42% of the valid votes polled and lost the election by 7,68,400 votes. If 82,560 votes were declared invalid and 20% people did NOT cast their vote, then the invalid votes were what percentage (rounded off to 1 decimal place) of the votes which people did NOT cast?

Learn how to calculate the percentage of invalid votes in an election where the defeated candidate secured 42% of valid votes, lost by 7,68,400 votes, and 20% of voters did not cast their vote. The problem involves using percentage and proportion concepts.

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