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.

Explanation:-

Winner gets 55% of votes.
As 4% votes were declared invalid so 96% would be the valid votes.
So,
Winner gets 55% of 96% valid votes.
Winner gets % valid votes = (55*96)/100 = 52.8% votes.
Loser gets = 96 - 52.8 = 43.2% votes.
Difference = 9.6%
Now, 9.6% = 4200.
So, 1% = 4200/9.66
Thus, 100% Votes = (4200 *100)/9.66 = 43750.
Hence, Total Voters = 43,750.

Alternatively,

Let total number of voters were X.
Invalid Votes = 4%.
Valid Votes = 96%.

Total Valid Votes = 96% of X = 96X/100 = 0.96X
Winner gets 55% of Valid Votes,
= (0.96 * 55)/100 = 0.528X votes.
Loser gets = (0.96X - 0.528X) = 0.432X.
Difference = 0. 528 - 0.432 = 0. 096X.
0.096X = 4200
X = 43750.
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