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In an election 4% of votes cast are invalid. A candidate gets 55% of casted votes and wins the election by 4200 votes. Find the total number of votes casted.

Correct Answer: 43750
Winner gets 55% of votesAs 4% votes were declared invalid so 96% would be the valid votesSo,Winner gets 55% of 96% valid votesWinner gets % valid votes = $$\frac{{55 \times 96}}{{100}}$$   = 52.8% votesLoser gets = 96 - 52.8 = 43.2% votesDifference = 9.6%Now, 9.6% = 4200So, 1% = $$\frac{{4200}}{{9.66}}$$Thus, 100% Votes = $$\frac{{4200 \times 100}}{{9.66}}$$   = 43750Hence, Total Voters = 43,750 Alternatively,Let total number of voters were X.Invalid Votes = 4%Valid Votes = 96%Total Valid Votes = 96% of X = $$\frac{{96{\text{x}}}}{{100}}$$  = 0.96XWinner gets 55% of Valid Votes, = $$\frac{{0.96 \times 55}}{{100}}$$   = 0.528X votesLoser gets = (0.96X - 0.528X) = 0.432XDifference = 0. 528 - 0.432 = 0. 096X0.096X = 4200∴ X = 43750

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