Question

A and B are two candidates in an election and a voter
can vote for either A or B. Candidate A gets 66.67%
of the votes got by candidate B. If only 90% of
eligible voters cast their vote and B gets 64800 more
votes than A, how many eligible voters were there?
.​

Answer 1

The Total Number of Eligible voters is 360042.

Given:

90% voters voted in election.

Candidate A get 66.67% votes of Candidate B.

Number of Votes of Candidate B - Number of Votes of Candidate A = 64800

To Find:

The Number of Eligible voters

Solution:

We have two candidates A and B.

Here Number of votes of candidate A = x

Number of votes of candidate B = y

Percentage of votes gotten by candidate A is 66.67% of that of Candidate B

So $x = \frac{66.67}{100} y$

Now difference between the votes of the two candidates is 64800

$y - x = 64800$

replacing for x, we get

$y - ( \frac{66.67}{100} y ) = 64800$

Taking y common we get,

$y ( 1 - \frac{66.67}{100} ) = 64800$

$y (\frac{100-66.67}{100}) = 64800$

$y (\frac{33.33}{100}) = 64800$

$y = \frac{100*64800}{33.33}$

$y = 194419$

The number of votes of B is 194419 so the number of vote of A is

$x=( \frac{66.67}{100} ) 194419$

$x = 129619$

So the total number of voters who voted is $x +y$

Total number of voters = $129619+194419$

$=324038$

This Number is  90% of all eligible voters.

So  $324038=\frac{90}{100}$ all eligible voters

All eligible voters = $\frac{324038*100}{90}$

=$360042$

So the Total Number of Eligible voters is 360042.

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