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.

Solution (By Examveda Team)

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 = $$\frac{{55 \times 96}}{{100}}$$   = 52.8% votes
Loser gets = 96 - 52.8 = 43.2% votes
Difference = 9.6%
Now, 9.6% = 4200
So, 1% = $$\frac{{4200}}{{9.66}}$$
Thus, 100% Votes = $$\frac{{4200 \times 100}}{{9.66}}$$   = 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 = $$\frac{{96{\text{x}}}}{{100}}$$  = 0.96X
Winner gets 55% of Valid Votes,
= $$\frac{{0.96 \times 55}}{{100}}$$   = 0.528X votes
Loser gets = (0.96X - 0.528X) = 0.432X
Difference = 0. 528 - 0.432 = 0. 096X
0.096X = 4200
∴ X = 43750