Question

In an election, $10\% $ of the people in the voter’s list did not participate. $60$ votes were declared invalid. There are only two candidates $A$ and $B$, $A$ defeated $B$ by $308$ votes. It was found that $47\% $ of the people listed in the voter’s list voted for $A$. Find the total no. of votes polled.
A.$6200$
B.$5580$
C.$6000$
D.$7200$

Answer 1

Hint: Total no. of votes polled will be equal to sum of the no. of voters voted for $A$ and the no. of voters voted for $B$. That is
Total no. of votes polled$ = $No. of voters voted for $A + $ No. of voters voted for $B$.
So, we just need to find out how many people voted for them from the given information then we will get our answer.

Complete step by step answer:
First of all we will start by enlisting the given information in the question.
So, it is given in the question that
Two candidates $A$ and $B$ participated in an election.
$A$ defeated $B$ by $308$ votes.
$10\% $ of the people in the voter’s list did not participate, $60$ votes were declared invalid.
$47\% $ of the people listed in the voter’s list voted for $A$.
So now, firstly let us assume that
No. of voters who voted for $A = x$
Then we can say by the given information that,
No. of voters voted for$B = x - 308$
Now, According to question we know that
$60$ votes were declared invalid.
$ \Rightarrow $Total no. of voters voted $ = $No. of votes of $A + $No. of votes of $B + $Total no. of Invalid votes
$ \Rightarrow $ Total no. of voters voted$ = x + x - 308 + 60$
$ \Rightarrow $ Total no. of voters voted$ = 2x - 248$ ………(i)
Now, as $10\% $ of the people in the voter’s list did not participate.
So, the percentage of total listed people participated will be equal to $90\% $
$ \Rightarrow $ $90\% $ of the people listed in the voter’s list$ = $Total no. of voters voted
$ \Rightarrow \dfrac{{90}}{{100}} \times $(No. of peoples listed in the voter’s list)$ = 2x - 248$ ……………{from (i)}
$ \Rightarrow $The no. of peoples listed in the voter’s list $ = \left( {2x - 248} \right) \times \dfrac{{100}}{{90}}$
$ \Rightarrow $The no. of peoples listed in the voter’s list $ = \dfrac{{\left( {20x - 2480} \right)}}{9}$
Now, further we know that
$47\% $ of the people listed in the voter’s list voted for$A$.
$ \Rightarrow $$47\% $ of the people listed in the voter’s list$ = x$
$
   \Rightarrow \dfrac{{47}}{{100}} \times \dfrac{{\left( {20x - 2480} \right)}}{9} = x \\
   \Rightarrow 47\left( {20x - 2480} \right) = 900x \\
   \Rightarrow 940x - 116560 = 900x \\
   \Rightarrow 40x = 116560 \\
 $
$ \Rightarrow x = 2914$
$ \Rightarrow $ No. of voters who voted for $A = 2914$
So, now from equation (i) we can say that
  Total no. of voters voted $ = 2x - 248$
$ \Rightarrow $ Total no. of voters voted$ = 2\left( {2914} \right) - 248$
$ \Rightarrow $ Total no. of voters voted$ = 5580$
$ \Rightarrow $ Option B is correct.


Note:
In these types of questions the trick to form equations is that by fixing a variable who’s all conditions are given, like here in this question we are given all the information of conditions of $A$ is given. So, by using that information we can find the no. of voters who voted for $A$.