Question

In an election, a candidate secured \[47\%\] of votes polled and lost the election by \[12,366\] votes. Find the total votes polled and the votes secured by the winning candidate.
A. $2,06,133$ and $1,09,266$
B. $2,16,100$ and $1,19,233$
C. $2,06,100$ and $1,09,233$
D. $2,06,233$ and $1,09,200$

Answer 1

Hint: In order to find a solution to this problem, we will have to first convert this word problem into mathematical format. After converting into mathematical form, we will have to create an expression. After we have all things we require, we will have to complete calculation of our expression to get the required answer.

Complete step by step answer:
As we know, we have our problem as a word problem, so we will first convert it into a mathematical problem.
Therefore, breaking down our problem into parts, we get:
Let the total votes be $V$.
If the losing candidate secured \[47\%\] of the votes, then the winning candidate won \[100-47=53\%\] of the votes.
Therefore, we can write our expression as:
$\Rightarrow \dfrac{53}{100}V-\dfrac{47}{100}V=12366$
Therefore, on solving our expression, we get:
$\Rightarrow \dfrac{6}{100}V=12366$
On simplifying, we get:
$\Rightarrow V=\dfrac{12366\times 100}{6}$
Therefore, we get total number of votes as:
$\Rightarrow V=206100$
So, total votes are $206100$.
Also, we have to find the votes secured by the winning candidate. The winning candidate won $53\%$ of $206100$. Therefore, we get:
 $\Rightarrow \dfrac{53}{100}\times 206100$
On simplifying, we get votes secured by winning candidate as:
$\Rightarrow 109233$
Therefore, votes secured by the winning candidate is $109233$.

So, the correct answer is “Option C”.

Note: A word problem is a few sentences that describes a 'real-life' scenario, where a problem needs to be solved in a way of a mathematical calculation. To solve a word problem, we have to read it well. One reason students struggle is because they have trouble with reading in general and not understanding the problem. Therefore, to turn a word problem into a number sentence, we need to understand the language and concepts of math first, then we can easily solve any word problem.