Two candidates X and Y contested an election. 80% of voters cast their vote and there were no invalid votes. There was no NOTA (None of the above) option. X got 56% of the votes cast and won by 1440 votes. What is the total number of voters in the voters list?

Correct Option

Let the total number of voters in the voters list be $T$.

According to the problem statement:

• 80% of voters cast their vote.
• Total votes cast = $80\mathrm{\%}$ of $T=\frac{80}{100}\times T=0.8T$.
• Candidate X received 56% of the votes cast.
• Candidate Y received $(100\mathrm{\%}-56\mathrm{\%})=44\mathrm{\%}$ of the votes cast.
• The winning margin for X was 1440 votes.

The difference in votes between Candidate X and Candidate Y equals the winning margin:

Votes for X - Votes for Y = 1440

$56\mathrm{\%}$ of $(0.8T)-44\mathrm{\%}$ of $(0.8T)=1440$

$(56\mathrm{\%}-44\mathrm{\%})$ of $(0.8T)=1440$

$12\mathrm{\%}$ of $(0.8T)=1440$

This can be written as:

$$1440=\frac{12}{100}\times \frac{8}{10}T$$

To solve for $T$:

$T=\frac{1440\times 100\times 10}{12\times 8}$

$T=\frac{1440000}{96}$

$$T=15000$$

Therefore, the total number of voters in the voters list is 15000.

Incorrect Options

Options 2 (12000), 3 (9600), and 4 (5000) are incorrect because they do not satisfy the conditions derived from the problem statement regarding the percentage of votes cast, the vote distribution between candidates X and Y, and the specified winning margin of 1440 votes.