Question

Two candidates were participating in an election. Of the total number of people in the electoral roll in that election, 10% did not use their votes and 60 votes were declared invalid. The winning candidate secured 47% of the total votes of the voter list and he won the election by 308 votes. How many votes were cast in that election ?
A. 6200
B. 5580
C. 6000
D. 7200

Answer 1

Hint: We will carefully see the question and analyze it , we will use the conditions given in the question. We will start by assuming the number of votes A gets as x. Then we will apply the condition that the defeated person gets 308 less votes then we will apply the condition that 90% of the list population took part in the election and then finally we will apply that 47% of the population voted for A.

Complete step by step answer:
Let the two candidates be A and B, let A be the candidate who won.
Now, let the number of votes A get$=x$
Now, it is given in the question that the defeated candidate, that is B, gets 308 less votes therefore : B gets $=x-308$
Now it is given that 60 votes were invalid, therefore, the total number of votes polled will be votes casted to A plus votes casted to B and then the 60 invalid votes: $x+x-308+60=2x-248\text{ }........\left( 1 \right)$
Now, it is given that 10% of the listed population refrained from voting , therefore 90% of the listed population took part in the election. Let the total population be P , therefore:
$\dfrac{90}{100}\times P=2x-248\Rightarrow P=\left( 2x-248 \right)\times \dfrac{100}{90}\Rightarrow P=\dfrac{20x-2480}{9}$
Now, 47% of this population voted for A , since A got a total of $x$ votes , therefore:
$\begin{align}
  & \Rightarrow \dfrac{47}{100}\times \dfrac{20x-2480}{9}=x \\
 & \Rightarrow 47\left( 20x-2480 \right)=900x\Rightarrow 940x-116560=900x \\
 & \Rightarrow 40x=116560 \\
 & \Rightarrow x=2914 \\
\end{align}$
So, the total numbers of votes polled are $2x-248$ from equation 1 , therefore we will put the value of $x$ in this equation, therefore: $\left( 2\times 2914 \right)-248=5580$

So, the correct answer is “Option B”.

Note: There is no difficult calculation in this question but always be careful while applying the conditions given in the question. A student can make a silly mistake while writing down the equations, even a small mistake can lead to wrong answers. For example, if we mistake a negative sign with a positive sign that is $2x+248$ , then the answer will come out to be wrong.