Question

In an election, $15\% $ of voters did not vote. A candidate who got $62.5\% $ of votes cast was declared elected by 3400 votes. Then the total number of votes are :
A) $15000$
B) $16000$
C) $17000$
D) $19000$

Answer 1

Hint: In these types of questions, we will take the total number as a variable to ease our calculations. We will make equations according to questions and solve them.So for this question we are going to take the total number of votes as ‘x’.

Complete step by step solution:
Let the total number of votes = $x$
$15\% $voters did not vote, so votes polled = $85\% $of $x$= $\dfrac{{85}}{{100}}x$
Now, according to question,
Votes polled by winning candidate = $62.5\% $of $85\% x$
${V_{winning}} = \left( {\dfrac{{625}}{{1000}}} \right)\left( {\dfrac{{85}}{{100}}} \right)x$
${V_{winning}} = \left( {\dfrac{5}{8}} \right)\% $ of $85\% x$
Now, votes polled by losing candidate =
${V_{lo\sin g}} = \left( {1 - \dfrac{5}{8}} \right)\% $ of $85\% x$
${V_{lo\sin g}} = \left( {\dfrac{3}{8}} \right)\% $ of $85\% x$
We are given that the winning candidate was declared elected by $3400$votes.
${V_{winning}} - {V_{lo\sin g}} = 3400$
$\left( {\dfrac{5}{8} - \dfrac{3}{8}} \right)\% $ of $85\% x = 3400$
$\left( {\dfrac{1}{4}} \right)\left( {\dfrac{{85}}{{100}}} \right)x = 3400$
$x = \dfrac{{3400 \times 400}}{{85}}$
$x = 16000$
So, total number of votes are 16000
Additional Information:
We can also solve this question by calculations rather than taking percentage of all but the calculation will become difficult. So, it is easy to solve with writing percentages and calculate answers at the end.

Note: This is a statement type question and A statement is a group of words arranged to form a meaningful sentence. So, pay attention while writing equations from the question, the wrong equation will result in the wrong answer.