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?

Given:

Total votes polled = V

Invalid votes = V / 5

Valid votes = V - V / 5 = 4V / 5

A wins by 2500 votes or 10% of total votes over B.

90% of invalid votes would have been in favour of B.

Formula Used:

Total votes polled = Valid votes + Invalid votes

Margin = Votes of A - Votes of B

Calculation:

Let votes for A be A and votes for B be B.

From the given,

A - B = 2500

A = B + 2500

Also,

A - B = 10% of total votes

⇒ 2500 = 0.1V

⇒ V = 25000

Invalid votes = V / 5 = 25000 / 5 = 5000

Valid votes = 4V / 5 = 4 × 25000 / 5 = 20000

Let votes for A be A and votes for B be B.

A + B = 20000

Also, A = B + 2500

Substitute A in the equation A + B = 20000:

(B + 2500) + B = 20000

⇒ 2B + 2500 = 20000

⇒ 2B = 17500

⇒ B = 8750

⇒ A = B + 2500 = 8750 + 2500 = 11250

90% of invalid votes are in favour of B:

⇒ 0.9 × 5000 = 4500

If these votes were added to B:

New votes for B = 8750 + 4500 = 13250

New margin = A - New B = 11250 - 13250 = -2000

Percentage margin = (New margin / Total votes) × 100

Percentage margin = (-2000 / 25000) × 100

Percentage margin = -8%

B would have won by 8%.