Question

In an election between two candidates ,10%of the voter didnot cast their votes .10% of the vote polled were found invalid.The successful candidates got 54% of the valid votes and won by majority of 1620,find the number voters enround on the voter list

Answer 1

Hii dear,
_________

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Let the total number of voters in the list be x.

Number of voters who did not cast their vote = 10% of x = 
$\frac{x}{10}$


So, total number of votes polled by voters = x - 
$\frac{x}{10}$
 = 
$\frac{9x}{10}$


Number of voters whose votes were found invalid = 10% of total votes polled =  
$\frac{10}{100} \times \frac{9x}{10} = \frac{9x}{100}$


So, total number of valid votes = 
$\frac{9x}{10} - \frac{9x}{100} = \frac{90x - 9x}{100} = \frac{81x}{100}$


Number of votes obtained by winner = 54% of 
$\frac{81x}{100} = \frac{54}{100} \times \frac{81x}{100}$


Number of votes obtained by the looser = 46% of 
$\frac{81x}{100} = \frac{46}{100} \times \frac{81x}{100}$


According to the question,

$\frac{54}{100} \times \frac{81x}{100} - \frac{46}{100} \times \frac{81x}{100}$
= 1620

⇒ 
$\frac{54 \times 81x}{10000} - \frac{46 \times 81x}{10000} = 1620$


⇒ 
$\frac{8 \times 81x}{10000} = 1620$


⇒ 
$\frac{8x}{10000} = 20$


⇒ 8x = 200000

⇒ x = 25000

Thus, the total number of voters in the list was 25,000.

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Answer 2

hope it helps...........