Q. 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?

Explanation : 

Two candidates X and Y contested an election

Let’s assume the total number of voters in the voter list as “T”.

80% of the voters cast their votes which means the total number of votes cast is (80/100) x T = 0.8T.

Now, we know that X got 56% of the votes cast, which means X got 0.56 x 0.8T = 0.448T votes.

Let’s assume Y got “y” votes. Since there were no invalid votes, the total number of votes cast is the sum of votes received by X and Y, i.e., 0.448T + y = 0.8T.

Solving for y, we get y = 0.352T.

Now, we know that X won by 1440 votes. This means X got 1440 more votes than Y. So, we can write an equation as:

0.448T – 0.352T = 1440

Simplifying the equation, we get 0.096T = 1440, which implies T = 15000.

Therefore, the total number of voters in the voter list is 15000, option (a) is the correct answer.