Question

In an election, the votes cast for two of the candidates were in the ratio 5:7. If the successful candidates received 20734 votes, how many votes did his opponents receive?

Answer 1

Given, the ratio of votes for two candidates = 5 : 7
Using equivalent ratio, we can find the actual number of votes for each candidate in the election.
We know the ratio of successful candidate must be greater than his opponent.
It means the ratio of votes of successful candidate to opponent candidate is 7 : 5
It is given that successful candidates received 20734 votes, which must be a mutiple of 7.
Lets say it is $x$ times of 7.
So, $7x$
Hence, $7x=20734$
$x=\frac{20734}{7}=2962$
Thus, $\frac{7\times 2962}{5\times 2962}=\frac{20734}{Votesreceivedbyopponent}$
Number of votes of his opponent = $5\times 2962$
= 14810