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?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. B would have won by 8%.
Let V represent the total votes polled.
Since every fifth vote is marked as invalid, the invalid votes are V/5
Therefore,
The valid votes = V - V/5 = 4V/5
Candidate A wins by a margin of 2500 votes, which is also given as 10% of the total votes
So, 10% of V
⇒ 10V/100 = 2500
⇒ V = 25000
Therefore, the total votes polled, V, is 25000.
Now,
Invalid Votes = V/5 = 25000/5 = 5000
Valid Votes = 4V/5 = 4 × 25000/5 = 20000
Given that A wins by 2500 votes
Valid votes of A - valid votes of B = 2500.....(1)
Also, the sum of valid votes for A and B is 20000
Valid votes of A + valid votes of B = 20000......(2)
from eq 1 and 2 we get,
⇒ 2 × Valid votes of A = 22500
Valid votes of A = 11250 then,
Valid votes of B = 20000 - 11250 = 8750
So,
90% of the invalid votes would have gone to B = 0.9 × 5000 = 4500
If these 4500 votes were added to B's total,
B’s new total = 4500 + 8750 = 13250
Since A's total remains 11250, B would now have more votes than A.
New margin = 11250 - 13250 = -2000
Now,
Percentage = New margin/Total votes × 100
⇒ -2000/25000 × 100
⇒ -8%
So,
B would have won by 8%