Question

In an election, two persons contested and the winner secured $58\%$ of the votes polled. If the difference between their votes is $8480$, find the votes secured by the winner.

Answer 1

Let the Votes got by the Winner be $x$

and the Votes got by Loser be $y$

Hence, Total Votes will be $x+y$

Now, it is given that $x-y=\mathrm{8480...........}\left(1\right)$

and $x=\frac{58}{100}(x+y)\Rightarrow \frac{58}{100}y=\frac{42x}{100}\Rightarrow 58y=42x\Rightarrow 29y=21x\Rightarrow x=\frac{29y}{21}.........\left(2\right)$

From (1) and (2)

$\frac{29y}{21}-y=8480\Rightarrow \frac{8y}{21}=8480\Rightarrow y=1060\ast 21=22,260$

Now, $x=\frac{29y}{21}=\frac{29\ast 1060\ast 21}{21}=29\ast 1060=30,740$

therefore, the winner secured 30,740 votes