In a certain assembly constituency election, $80\%$ of voters exercised their voting right and the winning candidate got elected with $65\%$ of votes polled. What percent of total votes did he poll?

### Concept & Logic This problem requires understanding nested percentages. The winning candidate's share is a percentage of the *polled* votes, which in turn is a percentage of the *total* voters. You must multiply the successive fractions/percentages to find the share relative to the total base. $$ \text{Total Percent} = \text{Polled \%} \times \text{Winner's Share of Polled \%} $$ ### Step-by-Step Solution * **Given:** * Voters who exercised their right (polled votes) = $80\%$ of total. * Winning candidate's share = $65\%$ of polled votes. * **Calculation:** * Let the total number of voters in the constituency be $100$. * Number of votes polled = $80\%$ of $100 = 80$. * The winning candidate received $65\%$ of these $80$ polled votes. * Winner's votes = $65\%$ of $80$ * $= \frac{65}{100} \times 80$ * $= 65 \times 0.8 = 52$ * Since the total number of voters was assumed to be $100$, the winning candidate's $52$ votes directly represent $52\%$ of the total votes. ### Exam Strategy & Shortcut Simply multiply the decimal equivalents of the percentages directly. $0.80 \times 0.65 = 0.52$ This translates immediately to $52\%$. You can do this mental math quickly by finding $10\%$ of $65$ ($6.5$), then subtracting $20\%$ ($13$) from $65$: $65 - 13 = 52$. ### Common Pitfall A common error is confusing the "percent of votes polled" with the "percent of total votes" and attempting to subtract $65\%$ from $80\%$ or finding $65\%$ of $100\%$. Always track what base amount a percentage is operating on. ### Final Answer **Therefore, the correct answer is 52.**