In an election between A and B, every fifth vote polled was marked as invalid by the machine. In the remaining votes, A wins the election with a margin of 2500 votes or 10% of the total votes polled, over B. If 90% of the invalid votes would have been in favour of B, then which of the following would have been the result of the election?

The correct answer is B would have won by 8%.

Let's solve this step-by-step carefully.

Step 1: Find the total valid votes polled.

We're told A wins over B in the remaining (valid) votes by a margin of 2500 votes, which also equals 10% of the total valid votes. (The "10% of total votes polled" here refers to the valid votes counted by the machine.)

So:

10\%\times \text{Valid Votes}=2500

\text{Valid Votes}=\frac{2500}{0.10}=\mathrm{25,000}

Step 2: Find the total votes polled (including invalid).

Since every 5th vote was invalid, invalid votes = 1/5 of total votes. So valid votes = 4/5 of total votes.

\frac{4}{5}\times \text{Total Votes}=\mathrm{25,000}

\text{Total Votes}=\mathrm{25,000}\times \frac{5}{4}=\mathrm{31,250}

\text{Invalid Votes}=\mathrm{31,250}-\mathrm{25,000}=\mathrm{6,250}

Step 3: Find A's and B's votes among the valid votes.

A wins by 2500 votes and total valid votes = 25,000:

\text{A}+\text{B}=\mathrm{25,000}

\text{A}-\text{B}=\mathrm{2,500}

Adding both equations:

2\times \text{A}=\mathrm{27,500}\Rightarrow \text{A}=\mathrm{13,750}

\text{B}=\mathrm{25,000}-\mathrm{13,750}=\mathrm{11,250}

Step 4: Distribute the invalid votes.

90% of invalid votes would have gone to B, and 10% to A:

\text{B's invalid share}=90\%\times \mathrm{6,250}=\mathrm{5,625}

\text{A's invalid share}=10\%\times \mathrm{6,250}=625

Step 5: Recalculate the true totals.

\text{A's total}=\mathrm{13,750}+625=\mathrm{14,375}

\text{B's total}=\mathrm{11,250}+\mathrm{5,625}=\mathrm{16,875}

Step 6: Determine the result and margin.

B leads A by:

\mathrm{16,875}-\mathrm{14,375}=\mathrm{2,500}\text{votes}

As a percentage of the total votes polled (31,250):

\text{Margin \%}=\frac{\mathrm{2,500}}{\mathrm{31,250}}\times 100=8\%

Conclusion: Had the invalid votes been counted with 90% going to B, B would have won the election by 8%. B's massive gain from the invalid votes (5,625 vs A's 625) flips the result entirely.