A candidate got 35% votes and lost to his opponent by 2250 votes. If there are only two candidates to vote for, how many votes were cast?

Explanation

Let the total number of votes be $x$. Votes received by the runner-up $= x \times \frac{35}{100}$ $\therefore$ votes received by the winner $$= x \times \frac{(100 - 35)}{100} = x \times \frac{65}{100}$$ According to the question $$x \times \frac{65}{100} - x \times \frac{35}{100} = 2250$$ $$\frac{30x}{100} = 2250$$ $x = 7500$