Question

In a municipal election, there were two candidates. One got 30% of the votes polled and was defeated by 16000 votes. Calculate the total number of votes polled.
(A) 24000
(B) 28000
(C) 30000
(D) 40000

Answer 1

Hint: First of all, let us assume that the total number of votes polled is x. The percentages of the total votes polled to the defeated candidate and the winning candidate are 30% and 70% respectively. Now, get the number of votes polled to the losing candidate and the winning candidate. It is given that one who got 30% of the total votes polled was defeated by 16000 votes. It means that the winning candidate had got 16000 more votes than the losing candidate. So, \[\dfrac{30}{100}x+16000=\dfrac{70}{100}x\] . Now, solve it further and get the value of x.

Complete step-by-step answer:
According to the question, it is given that in a municipal election, there were two candidates. One got 30% of the votes polled and was defeated by 16000 votes.
First of all, let us assume that the total number of votes polled is x.
The total number of votes polled = x ………………………………………..(1)
The percentage of the total votes polled to the defeated candidate = 30% ………………………………….(2)
30 % of the total votes were polled to the candidate who was defeated.
From equation (1), we have the total number of votes polled.
The number of votes polled to the losing candidate = 30% of x = \[\dfrac{30}{100}x\] ………………………………………(3)
From equation (2), we have the percentage of the total votes polled to the defeated candidate
The percentage of the total votes polled to the winning candidate = (100-30)% = 70% ………………………………………(4)
From equation (1), we have the total number of votes polled.
The number of votes polled to the losing candidate = 70% of x = \[\dfrac{70}{100}x\] ………………………………………(5)
From equation (3) and equation (5), we have the number of the votes that were polled to the losing candidate and the winning candidate respectively.
It is given that one who got 30% of the total votes polled was defeated by 16000 votes. It means that the winning candidate had got 16000 more votes than the losing candidate. So,
\[\begin{align}
  & \Rightarrow \dfrac{30}{100}x+16000=\dfrac{70}{100}x \\
 & \Rightarrow 16000=\dfrac{70}{100}x-\dfrac{30}{100}x \\
 & \Rightarrow 16000=\dfrac{40}{100}x \\
 & \Rightarrow \dfrac{16000\times 100}{40}=x \\
 & \Rightarrow 400\times 100=x \\
 & \Rightarrow 40000=x \\
\end{align}\]
From equation (1), we have the total number of the votes polled is equal to x.
Therefore, the total number of votes polled is equal to 40000.
Hence, the correct option is (D).

Note: In this question, one might make a silly mistake while forming the equation. One might add 16000 to \[\dfrac{70}{100}x\] and then make it equal to \[\dfrac{30}{100}x\] . This is wrong because it is given that one who got 30% of the total votes polled was defeated by 16000 votes. So, 16000 must be added to \[\dfrac{30}{100}x\] to make it equal to \[\dfrac{70}{100}x\] .