Question

In an election, there were only two candidates for the post of president. The winning candidate got 53% of the total votes. His opponent got 31000 votes which represented 31% of the total votes. Find (i) the number of votes and (ii) the winning margin

Answer 1

Hint: In this question, we are given the percentage of votes for the winning candidate and his opponent. We are also given the number of votes of the opponent. Using this, we need to find the number of votes of the winning candidate and the winning margin. For this, we will first assume the total votes as x and then use the percentage and the number of votes of the opponent to find the total votes. Then we will find the number of votes of the winning candidate given in the percentage and the total votes. At last, we will find the difference between the number of votes of the winning candidate and his opponent to find the required margin. We will use x % of y as \[\dfrac{x}{100}\times y.\]

Complete step-by-step answer:
Here, we are given that the winning candidate got 53% of the total votes and we need to find the number of votes to the winning candidate which means we need to find 53% of total votes. Let us assume that the total votes are x. So, we need to find 53% of x. But first, let us find the value of x. As, we know that 31% of total votes were given to the opponent. So, we can say that the number of votes to the opponent is 31% of x. We know that the number of votes to an opponent was 31000. Hence, 31% of x = 31000. As, x% of y can be written as \[\dfrac{x}{100}\times y,\] so we get,
\[\dfrac{31}{100}\times x=31000\]
Cross multiplying, we will get,
\[\Rightarrow 31x=31000\times 100\]
\[\Rightarrow 31x=3100000\]
Dividing both the sides by 31, we get,
\[\Rightarrow x=\dfrac{3100000}{31}\]
\[\Rightarrow x=100,000\]
Hence, the votes were 100,000. Now, the number of votes to the winning candidate was 53% of x. So, we need to find 53% of 100000, since x% of y is \[\dfrac{x}{100}\times y.\] Hence, we can write,
\[\Rightarrow \dfrac{53}{100}\times 100000=53000\]
Hence, the number of votes to the winning candidate is 53000. We also need to find the winning margin. The winning margin is written as
Winning Margin = Number of votes to winning candidate – Number of votes to the opponent
\[\Rightarrow \text{Winning Margin}=53,000-31,000\]
\[\Rightarrow \text{Winning Margin}=22,000\]
Hence, the winning margin was 22,000.

Note: Students should be careful while doing the calculations dealing with large numbers. While calculating x% of y, make sure to divide x by 100 and then multiply by y. Take care while calculating the winning margin. We need to find the difference between the votes of the winner and opponent and not between the total votes and the winner’s votes.