In an election $4 %$ of the votes cast are invalid. A candidate gets $55 %$ of the valid votes and wins the election by $1920$ votes. Find the number of votes cast

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Solution

Winner gets $55 %$ of votes
As $4 %$ votes were declared invalid. $96 %$ would be the valid votes
Winner gets $%$ valid votes:
$= \frac{55}{96} \times 100 = 52.8 %$ votes
Loser gets $= 96 - 52.8 = 43.2 %$ votes
Difference $= 52.8 - 43.2 = 9.6 %$
$9.6 % = 1920$
$1 % = \frac{1920}{9.6}$

$100 % = \frac{1920}{9.6} \times 100$
$= 20, 000$ .
Hence, the number of votes cast is 20,000

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In an election 4% of the votes cast are invalid. A candidate gets 55% of the valid votes and wins the election by 1920 votes. Find the number of votes cast

Winner gets 55% of votesAs 4% votes were declared invalid. 96% would be the valid votesWinner gets % valid votes:=5596×100=52.8% votesLoser gets=96−52.8=43.2% votesDifference =52.8−43.2=9.6%9.6%=19201%=19209.6100%=19209.6×100=20,000.Hence, the number of votes cast is 20,000

In an election $4 %$ of the votes cast are invalid. A candidate gets $55 %$ of the valid votes and wins the election by $1920$ votes. Find the number of votes cast