Question

in an election a candidate squared 55% of the votes polled and won 2554 votes.find the total number of votes polled and the votes secured by the winning candidate

Answer 1

$let \: the \: total \: number \: of \: votes \: = x \\ the \: winner \: got \: 55\% \: of \: x = 55 \times \frac{x}{100} = \frac{11x}{20} \\ and \: loser \: got \: 45\% \: of \: x = 45 \times \frac{x}{100} = \frac{9x}{20} \\ according \: to \: question \: \frac{11x}{20} = \frac{9x}{20} + 2554 \\ = > \frac{11x}{20} - \frac{9x}{20} = 2554 \\ = > \frac{2x}{20} = 2554 \\ = > x = 25540 \\ so \: total \: votes \: = 25540 \\ winner \: got \: \frac{11 \times 25540}{20} = 14047 \\ \: and \: loser \: got \: = \frac{9 \times 25540}{20} = 11493$