Question

10 % of the voter did not cast their vote in an election between two candidates. 10 % of the votes polled were found invalid. the successful candidate got 54 % of the valid votes and won by a majority of 1620 votes. the number of voters enrolled in the voter's list was

Answer 1

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Answer 2

Answer:

10% of the voters did not cast their vote in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes.

To Find:-

The number of voters enrolled on the voters list was

Solution:-

$\color{maroon} \rm \: Let \: the \: numer \:of \: votes \: enrolled \: be \: x$

No. of voters cast their vote=90% of x

No. of votes polled valid=90% of (90% of x)

It is given that the winner won by the majority of 1620 votes. So, 8% of the votes enrolled (valid votes) is 1620 .So,

$\begin{gathered} \therefore \: \rm 8\% \: of \{90\%(90\% \: of \: x) \} = 1620 \\ \looparrowright \rm \: \: \frac{8}{100} \times \frac{90}{100} \times \frac{90}{100} \times x = 1620 \\ \looparrowright \rm \:x = \cancel \frac{16200 \times 100 \times 100 \times 100}{8 \times 90 \times 90} \\ \looparrowright \rm \: \color{olive}x = 25000\end{gathered}$

$\large \bold{@WildCat7083}$