Question

$8\% $ of the voters in an election did not cast their votes. In the election, there were only two contestants. The winner by obtaining $48\% $ of the total votes defeated his contestant by $1100$ votes. The total number of the voters in the election was-
A) $21000$
B) $23500$
C) $22000$
D) $27500$

Answer 1

Hint:
Fist, assume the total number of votes to be a. Since $8\% $ of the voters in an election did not cast their votes so find the numbers of votes actually cast. Then find the number of votes obtained by the winner. Subtract it from the total votes actually cast to get the number of votes obtained by the other candidate. Then we can write that the number of votes the winner got will be equal to the sum of the number of votes the other candidate got and the number of votes by which he was beaten. Put the obtained values and solve for a.

Complete step by step solution:
Given, there are only two candidates in the election.
The percentage of voters who did not cast their votes= $8\% $
The winner obtained $48\% $ of the total votes and defeated his contestant by $1100$ votes.
We have to find the total number of voters in the election.
Let us assume the total number of votes is a.
Now, given that the winner has obtained $48\% $ of the total votes so he has the number of votes=$\dfrac{{48a}}{{100}}$
But $8\% $ of the voters in an election did not cast their votes so the number of votes the winner got=$a - \dfrac{{8a}}{{100}}$
On solving we get-
The number of votes actually given=$\dfrac{{100a - 8a}}{{100}}$
On subtraction, we get-
The number of votes actually given=$\dfrac{{92a}}{{100}}$
Then the number of votes the other candidate got= Total number of votes cast- the number of votes the winner got
On putting the values, we get-
Number of votes the other candidate got=$\dfrac{{92a}}{{100}} - \dfrac{{48a}}{{100}}$
On taking LCM, we get-
Number of votes the other candidate got=$\dfrac{{92a - 48a}}{{100}} = \dfrac{{44a}}{{100}}$
Now, given that the other candidate lost by $1100$ votes.
So the number of votes the winner got will be equal to the sum of the number of votes the other candidate got and the number of votes by which he was beaten.
So we can write-
$ \Rightarrow \dfrac{{48a}}{{100}} = \dfrac{{44a}}{{100}} + 1100$
On solving we get-
$ \Rightarrow \dfrac{{48a}}{{100}} - \dfrac{{44a}}{{100}} = 1100$
On subtraction, we get-
$ \Rightarrow \dfrac{{44a - 44a}}{{100}} = 1100 \Rightarrow \dfrac{{4a}}{{100}} = 1100$
On simplifying we get-
$ \Rightarrow a = \dfrac{{1100 \times 100}}{4}$
On further simplifying we get-
$ \Rightarrow a = 275 \times 100 = 27500$

The correct answer is D.

Note:
Here we can also solve this question by this solving in terms of percentage -
The percentage of votes cast will be=total percentage of votes- the percentage of voters who didn’t cast votes.
So the percentage of total votes cast=$100\% - 8\% = 92\% $
Now out of this $48\% $ votes were obtained by the winner then the loser got votes= $92\% - 48\% = 44\% $
So the difference between the votes obtained by the winner and the other candidate is $4\% $ and it is given that the winner beat the other candidate by $1100$ votes. So we can say that-
$ \Rightarrow 4\% $ of the total votes=$1100$
Then total votes =$\dfrac{{1100}}{{4\% }} = \dfrac{{1100 \times 100}}{4}$
On solving we get the total number of votes=$27500$