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?

The correct option is 15000.

Let us break down the solution step-by-step to understand how to find the total number of voters in the voters list.

Step 1: Understand the voting breakdown
Let the total number of voters in the voters list be represented by $V$.
According to the problem, only 80% of the total voters cast their votes. Therefore, the total number of votes cast is:
$\text{Votes Cast}=80\%\text{of}V=0.80V$

Step 2: Determine the votes received by each candidate
There were no invalid votes and no NOTA option, meaning all votes cast went to either candidate X or candidate Y.
Candidate X received 56% of the votes cast. Therefore:
$\text{Votes for X}=56\%\text{of Votes Cast}$
Since the total percentage of votes cast is 100%, candidate Y must have received the remaining percentage of the votes cast:
$\text{Votes for Y}=(100-56)\%\text{of Votes Cast}=44\%\text{of Votes Cast}$

Step 3: Analyze the margin of victory
Candidate X won the election by 1440 votes. The difference in the percentage of votes cast received by X and Y is:
$\text{Difference}=56\%-44\%=12\%\text{of Votes Cast}$
We are given that this difference corresponds to 1440 votes:
$12\%\text{of Votes Cast}=1440$

Step 4: Calculate the total votes cast
Using the relation from Step 3, we can find the total votes cast:
$0.12\times \text{Votes Cast}=1440$
Dividing both sides by 0.12:
$\text{Votes Cast}=\frac{1440}{0.12}=12000$

Step 5: Calculate the total number of voters in the list
We know from Step 1 that the votes cast represent 80% of the total voters list ($V$):
$0.80V=12000$
Now, solve for $V$ by dividing 12000 by 0.80:
$V=\frac{12000}{0.80}=15000$

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