Question

One candidate in an election got 1200 votes. The other candidate got 60% of the total votes. If the election had only two candidates, how many total votes were there?​

Answer 1

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\huge{\underline{\color{red}{\rm{Question}}}}}$

One candidate in an election got 1200 votes. The other candidate got 60% of the total votes. If the election had only two candidates, how many total votes were there?

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\huge{\underline{\color{green}{\bf{Required\:Answer}}}}}$

${\large{\boxed{\color{pink}{\sf{3000\:votes}}}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\large{\underline{\underline{\color{orange}{\sf{Given}}}}}}$

${\large{\sf{The\:first\:candidate\:got=1200\:Votes}}}$

${\large{\sf{Given\:percentage\:of\:other\:canditate=60\:percent}}}$

${\large{\sf{\therefore first\:candidate\:got=100-60=40\:percent}}}$

${\large{\underline{\underline{\sf{To\:Find}}}}}$

${\large{\sf{Total\:votes\:performed=?}}}$

${\large{\underline{\underline{\sf{Formula\:Using}}}}}$

${\large{\underline{\boxed{\color{red}{\sf{To\:Find\:percentage=\dfrac{Number\:of\:votes\:of\:1^{st}\:candidate}{Percentage\:of\:votes\:1^{st}\:Candidate}}}}}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\qquad{\qquad{\qquad{\large{\underline{\underline{\color{blue}{\frak{Solution}}}}}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

${\qquad{\qquad{\qquad{\large{\color{grey}{\sf{Finding\:one\:percent}}}}}}}$

${\qquad{\qquad{\large{\sf{To\:Find\:percentage=\dfrac{Number\:of\:votes\:of\:1^{st}\:candidate}{Percentage\:of\:votes\:1^{st}\:Candidate}}}}}}$

${\qquad{\qquad{\large{\sf{1\:percent=\dfrac{Votes}{percent}}}}}}$

${\qquad{\qquad{\large{\sf{1\:percent=\dfrac{1200}{40}}}}}}$

${\qquad{\qquad{\large{\sf{1\:percent=30\:vote}}}}}$

${\qquad{\qquad{\large{\sf{1200\:is\:canceled\:by\:40\:resulting\:30}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

${\large{\underline{\boxed{\color{green}{\sf{1\:vote}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{1\:percent :\implies\:30\:votes}}}}}}$

${\qquad{\qquad{\large{\sf{1\:percent=30\:vote}}}}}$

${\qquad{\qquad{\large{\sf{\therefore 60\:percent=60\:times 30}}}}}$

${\qquad{\qquad{\large{\sf{1800}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

${\large{\underline{\boxed{\color{green}{\sf{Number\:of\:votes\:in\:favor\:of\:2^{nd}\:candidate :\implies 1800}}}}}}$

${\qquad{\qquad{\large{\color{grey}{\sf{Total\:Number\:of\:Votes:}}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

${\qquad{\qquad{\quad{\large{\sf{favor\:of\:1^{st}candidates+favor\:of\:2^{nd}candidates}}}}}}$

${\qquad{\qquad{\quad{\large{\sf{1200+1800}}}}}}$

${\qquad{\qquad{\quad{\large{\sf{3000}}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

${\large{\underline{\boxed{\color{green}{\sf{Total\:number\:of\:votes:\implies 3000\:votes}}}}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$