Question

In an election 4% of the votes cast are invalid. A candidate gets 55% of the total valid votes and wins the election by 1920 votes. Find the number of votes cast. (There are only two candidate)​

Answer 1

Answer:

43750

Step-by-step 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.