Question

There were two candidates in an election, $20\%$ of the numbers in the voters list did not cast their votes and $50$ votes were declared in valid. The successful candidates secured $300$ votes more than his rival. If $45\%$ of the total members voted in favour of successful candidates then find the votes secured by each candidates.

Answer 1

Let first candidate got $m$ votes and other candidate was successful and got $n$ votes.

Invalid votes $:60$

Total number of voters in the list $=N$

No Voting or absentees$:N\times \frac{20}{100}=0.2N$

Total number of VALID votes $=n+m$

Total number of polled votes $=(n+m+60)=80\%ofN=0.8N$

So,

$n+m=0.8N-50$ ......(1)

$n=m+300$

$n-m=300$ ......(2)

On adding equation (1) and (2), we get

$2n=0.8N+300-50\Rightarrow 0.8N+250$

$n=0.40N+125$ ......(3)

$n=45\%ofN=0.45N$ ......(4)

$0.40N+125=0.45N$ [from equation (3)]

$125=0.05N$

Hence,

Total votes $N=2,500$

Successful candidate got $n=0.45\times 2,500\Rightarrow 1,125$ votes

First candidate got $m=1,125-300\Rightarrow 825$ votes.