Question : In an election, a candidate secures 42% of the votes polled but is defeated by his only opponent by a majority of 3080 votes, because of 1400 invalid votes. The percentage of invalid votes is _______.
Option 1: 5%
Option 2: 3%
Option 3: 4%
Option 4: 6%
Correct Answer: 5%
Solution :
Let the total number of valid votes polled as $100x$.
The candidate secured 42% of the votes, which means his opponent's votes and 1400 comprises of remaining 58% of the votes. The difference between the votes secured by the opponent and the candidate is given as 3080 votes.
$⇒58x - 42x = 3080+1400$
$⇒x = 280$
So, the total number of valid votes polled = $100x = 28000$
The percentage of invalid votes = $\frac{1400}{28000}$ × 100 = 5%
Hence, the correct answer is 5%.
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