Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?

### Concept & Formula This problem requires calculating a simple percentage share. The core formula to find the percentage share of a specific part out of a whole is: $$ \text{Percentage} = \left( \frac{\text{Part Value}}{\text{Total Value}} \right) \times 100 $$ ### Step-by-step Solution **Given:** Votes for Candidate 1 = 1136 Votes for Candidate 2 = 7636 Votes for Candidate 3 (Winner) = 11628 First, calculate the total number of votes polled in the election: Total Votes = $1136 + 7636 + 11628$ Total Votes = $20400$ The winning candidate is the one with the maximum votes, which is 11628. Now, calculate the winning candidate's percentage of the total votes: $$ \text{Winning Percentage} = \left( \frac{11628}{20400} \right) \times 100 $$ Simplify the fraction by canceling the zeros: $$ = \frac{11628}{204} $$ Perform the division: $11628 \div 204 = 57$ ### Exam Strategy & Shortcut Use the **Approximation Method** to avoid tedious long division. Total votes $ \approx 20,400 $. Winner's votes $ \approx 11,600 $. Fraction $ \approx \frac{11.6}{20.4} \approx \frac{11.6}{20} $. $ \frac{11.6}{20} = \frac{116}{200} = \frac{58}{100} = 58\% $. Looking at the options, 57% is extremely close to 58%, making it the obvious choice without doing exact arithmetic. ### Common Pitfall Students sometimes calculate the percentage based only on the combined votes of the losing candidates rather than the grand total of all votes cast. Always ensure your denominator represents the total ecosystem. ### Final Answer **Therefore, the correct answer is 57%.**