Question

In a straight contest, the loser polled 42% votes and lost by 14400 votes. Find the total number of votes polled. If the total number of eligible voters was 1 lakh, find what percentage of voters did not vote.

Answer 1

Hint: In this question, we have to find two things.
First, we have read the given data clearly.
Also, we have to find loser and winner votes and subtract that into the total number of votes by lost. We get the answer and also we will find the percentage of voters who did not vote.

Formula used:
Percentage $ = \dfrac{{{\text{total no of eligible votes }}}}{{{\text{total no of votes }}}} \times 100$

Complete step by step answer:
Let us assume that the number of votes polled be $x$
It is given that Loser got the votes $42\%$ of $ x$
Here we have to convert into
$ \Rightarrow \dfrac{{42}}{{100}}x$
Now, we have to find the number of winners.
Here we have to subtract the lost in the total.
So we can write it as, \[{{(100 - 42) \% x = 58\%}}\] of \[x\]
Therefore, the number of winners is \[58\% {\text{ of }}x\]
Now we have to convert into,
$ \Rightarrow \dfrac{{58}}{{100}}x$
Also in the given, the margin by which the loser lost is equal to \[14400\].
Now we have to find the total number of votes polled.
So we have to know the difference between winners and loser's vote is equal to \[14400\].
\[ \Rightarrow \dfrac{{58x}}{{100}} - \dfrac{{42x}}{{100}} = 14400\]
Let us take the denominator terms as common and we get,
\[ \Rightarrow \dfrac{{\left( {58x - 42x} \right)}}{{100}} = 14400\]
On subtracting the numerator terms, we get
\[ \Rightarrow \dfrac{{16x}}{{100}} = 14400\]
By cross-multiplication,
\[ \Rightarrow 16x = 14400 \times 100\]
Taking the variable as LHS and remaining as RHS, we can write it as,
\[\; \Rightarrow x = \dfrac{{14400 \times 100}}{{16}}\]
On some simplification we get
\[ \Rightarrow x = 90000\]
Hence, the total no of votes polled is $90000$
Also, we have to find out the percentage of voters who did not vote.
It is given that the number of eligible voters = \[100000\]
Now we have to subtract the number of eligible voters and the total no of votes polled,
We get the number of voters who didn't vote
\[ = 100000 - 90000\]
On subtracting the terms we get
\[ = 10000\]
Here we have to find out the percentage, by using the formula we get
The percentage of voters, who didn't vote,
$ \Rightarrow \dfrac{{10000}}{{100000}} \times 100$
On simplification we get,
$ \Rightarrow 10\% $

$\therefore$ The percentage of voters who did not vote is $10\% $.

Note:
 Here we have to find the same question by using another method as follows,
Let us assume the number of votes polled is $100$
Here the given data is Loser got the votes \[42\]
We have to find the winner got the vote so we have to subtract it in the total count and we get,
\[ = 100 - 42 = 58\]
The difference of the votes between losers and winners is $16$

Number of votes polled	Their difference
\[x\]	\[14400\]
\[100\]	$16$

When Votes polled is 100 and the difference is $16$.
Therefore, when the difference is $14400$, and the votes polled will be \[x\]
$ \Rightarrow \dfrac{{100}}{{16}} = \dfrac{x}{{14400}}$
By cross-multiplication,
$ \Rightarrow 16x = 14400 \times 100$
Taking the variable as LHS and remaining as RHS we can write it as,
 \[\; \Rightarrow x = \dfrac{{14400 \times 100}}{{16}}\]
On some simplification we get,
\[ \Rightarrow x = 90000\]
 Hence the total no of votes polled is $90000$.