In an election between two candidates, the defeated candidate secured 40% of the valid votes polled and lost the election by 8,64,000 votes. If 76,000 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?

Sure, let's break it down:

Step 1: We know that the defeated candidate secured 40% of the valid votes and lost by 864,000 votes. This means that the winning candidate secured 60% of the valid votes. Therefore, the difference between 60% and 40% of the valid votes is 864,000 votes.

Step 2: We can set up the equation 0.2 * (total valid votes) = 864,000 to find the total number of valid votes. Solving this equation gives us a total of 4,320,000 valid votes.

Step 3: We know that 76,000 votes were declared invalid. So, the total number of votes cast (valid + invalid) is 4,320,000 + 76,000 = 4,396,000 votes.

Step 4: We also know that 20% of people did not cast their vote. This means that the total number of people who could vote (those who voted + those who did not vote) is 100% / 80% * 4,396,000 = 5,495,000 people.

Step 5: The number of people who did not vote is 20% of this total, or 1,099,000 people.

Step 6: Finally, we can find the percentage of invalid votes out of the votes which people did not cast by dividing the number of invalid votes by the number of people who did not vote and multiplying by 100: (76,000 / 1,099,000) * 100 = 6.9%.

So, the invalid votes were approximately 6.9% of the votes which people did not cast.