In an election 8%of the votrs didnt cast their votes.the winner by obtaining 52%of the total votes(cast+non cast)defeated his sole rival by...

We are given that in the election 8% of the voters did not
vote. Let the total number of eligible voters be N. So the number of people who voted is
N*(1-.08) = 0.92*N .

Now the winner has 52% of the total
votes that could be cast or the number of votes he has is
0.52*N

The loser got the rest of the votes, so he got
(0.48-.08)*N= 0.4*N of the votes.

Now the number of votes
that the winner got is 120 more than the loser, so 0.52*N - 0.4*N =
120

Hence N*( 0.52 - 0.4) =
120

=> N = 120 /
.12

=> N = 1000

As the
winner got 52% of these votes the number of votes he got is 0.52*1000=
520

The winner got 520
votes.