Question : In an election between two candidates, 10% of the voters in the voter list did not cast their vote, whereas 10% of the votes cast were found to be invalid. The winning candidate got 56% of the valid votes and won the election by a margin of 1458 votes. What is the total number of voters enrolled in the voter list?
Option 1: 14000
Option 2: 15000
Option 3: 16000
Option 4: 13000
Correct Answer: 15000
Solution :
Let the number of voters be $x$.
As 10% of the voters did not cast their vote,
The votes polled = 90% of $x$
As 10% of the votes polled were found to be invalid,
Valid votes = 90% of (90% of $x$)
If the winning candidate got 56% of the valid votes, then the other candidate got 44% of the valid votes.
56% of [90% of (90% of $x$)] − 44% of [90% of (90% of $x$)] = 1458
⇒ 12% of [90% of (90% of $x$)] = 1458
⇒ $\frac{12}{100} \times \frac{90}{100} \times \frac{90}{100} \times x = 1458$
$\therefore x = \frac{1458 \times 100\times 100 \times 100}{12\times 90\times 90} = 15000$
Hence, the correct answer is 15000.
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