Question : In an election between two candidates, 20% of the voters on the voter's list did not cast their votes and 80 voters cast their ballot papers blank. The winner secured 45% of all the voters in the list and he got 280 votes more than his rival. The number of voters on the list was:
Option 1: 1500
Option 2: 2800
Option 3: 2500
Option 4: 2000
Correct Answer: 2000
Solution : Given : 20% of voters did not cast their votes. 80 voters cast their ballot papers blank. The winner gets 45% votes of the total voters and wins by 280 votes. Now, Let the total number of votes in the voting list be $x$. Total cast votes $=x\ \times \frac{(100\ -\ 20)}{100}\ = 80x$ Total valid votes = $80x\ - 80$ Number of votes winner got = $x\ \times \frac{45}{100}\ = 45x$ Number of votes loser got = $45x\ -\ 280$ According to the question, $\Rightarrow 0.45x\ +\ 0.45x\ -\ 280\ =\ 0.80x\ -\ 80$ $\Rightarrow 0.90x\ -\ 280\ =\ 0.80x\ -\ 80$ $\Rightarrow 0.10x\ = 200$ $\therefore x\ =\ 2000$ Hence, the correct answer is 2000.
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