Question

There are two candidates in an election. $11\%$ of the voters did not vote. $500$ votes were declared invalid. The elected candidate got $3300$ votes more than his opponent. If the elected candidate got $48\%$ of the total votes, how many votes did each candidate get ?

Answer 1

Let there are total $x$ votes
Elected candidate gets $48\%$of total votes.
$=48\%$ of $x=\left(\frac{48x}{100}\right)$ votes
Opponent vote $=\left(\frac{48x}{100}\right)-3300$
Invalid votes $=500$
Voters did not vote $11\%$ of $x=\frac{11x}{100}$
So, total votes $=x$
$\Rightarrow \left(\frac{48x}{100}\right)+\left(\frac{48x}{100}\right)-3300+500+\frac{11x}{100}=x$
$\Rightarrow \frac{(48x+48x+11x)}{100}=2800+x$
$\Rightarrow 107x=280000+100x$
$\Rightarrow 7x=280000$
$\Rightarrow x=40000$
Total votes $=40000$
Winner's votes $=\frac{(48\times 40000)}{100}=19200$ votes
Loser's votes $=19200-3300=15900$ votes.