Question

In an election between two candidates, the candidate who gets 30% of the votes polled is defeated by 15,000 votes. What is the number of votes polled by the winning candidate?
(a). 11,250
(b). 15,000
(c). 26,250
(d). 37,500

Answer 1

We should first assign a variable to the total number of polled votes in the election. Then we can separately write which candidate got how many votes. Then we can form an equation to find the total number of polled votes.

Complete step-by-step answer :
Let us assume the total number of polled votes to be ‘x’. Now we can write the votes polled by losing candidate to be $30\%ofx$ and the votes polled by winning candidate is $x-(30\%ofx)$ .
In the question it is given that the losing candidate lost by 15,000 votes means the winning candidate has 15,000 more votes than the losing candidate.
Now we can write, votes polled by winning candidate to be $30\%x+15,000$ which is equal to $x-(30\%ofx)$ .
Therefore, we can form the following equation:
$30\%x+15,000=x-(30\%ofx)$
We know $30\%=\dfrac{30}{100}=\dfrac{3}{10}$ . On substituting this value we get,
$\begin{aligned} & 30\%x+15,000=x-(30\%x) \\\ & \Rightarrow \dfrac{3x}{10}+15000=x-\dfrac{3x}{10} \\\ \end{aligned}$
On simplifying we get,
$\begin{aligned} & x-2\cdot \dfrac{3x}{10}=15000 \\\ & \Rightarrow x-\dfrac{3x}{5}=15000 \\\ & \Rightarrow \dfrac{2x}{5}=15000 \\\ & \Rightarrow x=\dfrac{5\times 15000}{2} \\\ \end{aligned}$
On calculating we get,
$x=37,500$
Now we have the total number of polled votes. Now we will calculate the votes polled by winning candidate which is- $30\%x+15,000\Rightarrow \dfrac{3x}{10}+15000$
Substituting the value of x we get,
$\dfrac{3x}{10}+15000=\dfrac{37500\times 3}{10}+15000$
On calculating we get the number of votes polled by the winning candidate to be 26,250.
Hence, the correct option is (c).

Note : We can easily commit the following mistake in haste. As we can see all the options that we are given occurs while calculating in our solution body. If we mistakenly calculate x and forget that it is not votes polled by winning candidate but total number of votes polled then we will choose (d) and it will be the wrong answer or if calculate the votes polled by losing candidate and forget to add the extra 15000 then we will choose (a) which will also be wrong.