In a municipality election, two candidates contest. One of them receives 54% of the total votes polled and wins by a margin of 1080 votes. What is the total number of votes polled in the election?

Introduction / Context:
This problem is a standard election percentage question. There are two candidates, one of whom secures a known percentage of the total votes. The margin of victory in terms of votes is also known. We are asked to find the total number of votes polled. Questions of this type are common in entrance exams and competitive tests, as they combine percentage understanding with basic algebra.

Given Data / Assumptions:

Only two candidates contest the election.

The winning candidate gets 54% of the total votes.

The losing candidate therefore gets the remaining 46% of the total votes.

The margin of victory, that is the difference between their vote counts, is 1080 votes.

We need to find the total number of votes polled.

Concept / Approach:
If the total number of votes is V, then the winner receives 0.54V votes and the loser receives 0.46V votes. The difference between these two quantities equals the given margin of 1080 votes. So we form the equation (0.54V - 0.46V) = 1080. The left side simplifies to a certain percentage of V, and solving this equation gives the total number of votes. This direct approach avoids unnecessary steps and is very efficient.

Step-by-Step Solution:
Let the total number of votes polled be V.Votes for winner = 54% of V = 0.54V.Votes for loser = 46% of V = 0.46V.Margin of victory = votes for winner minus votes for loser.So, margin = 0.54V - 0.46V = 0.08V.We are given that margin = 1080 votes.Therefore, 0.08V = 1080.So V = 1080 / 0.08.Compute 1080 / 0.08 = 1080 * (100 / 8) / 100 = 13500.Thus, the total number of votes polled is 13,500.

Verification / Alternative check:
Check by computing the individual vote counts. With V = 13,500, winner's votes = 54% of 13,500 = 0.54 * 13,500 = 7,290. Loser's votes = 46% of 13,500 = 0.46 * 13,500 = 6,210. The difference is 7,290 - 6,210 = 1,080 votes, which matches the given margin. Therefore, V = 13,500 is correct.

Why Other Options Are Wrong:

12,000 would give a margin of 8% of 12,000, which is 960, not 1,080.

15,400 would give a margin of 8% of 15,400, which is 1,232, not 1,080.

11,000 would give a margin of 8% of 11,000, which is 880, also incorrect.

14,500 would give a margin of 8% of 14,500, equal to 1,160, again not matching 1,080.

Common Pitfalls:
Some students mistakenly equate 54% directly to 1080 votes and then scale incorrectly. Others forget that the margin corresponds to the difference between the two percentages, that is 54% minus 46% = 8%. Another error is to miscalculate 8% of a number when working backwards. Always clearly define the total as V, express both candidates' vote counts in terms of V, and set their difference equal to the given margin.

Final Answer:
The total number of votes polled in the election is 13500.