# 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 120votes.how many votes did the winner get?

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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.**

Let x be the tototal votes cast.

The number of peersons whodid not cast = 8% of x = 0.8x perrsons.

The votes polled by the winner = 52% of x = 0.52x.

So the number of votes polled by the person defeted = {x - (0.52x+0.08x)} = 0.40x.

Therefore the number of more votes by which winner exceeded the rival = 0.52x-0.40x but this is given to be 120.

Therefore 0.52x-0.40x = 120.

0.12x = 120.

x = 120/0.12 = 1000.

The votes poleed = 1000.

Number of votes got by the winner = 0.52x = 520.

Let the total number of voters be= 100v

8% did not cast votes so 8v did not cast votes

=> 100v-8v= 92v cast votes.

winner obtained 52% votes = 52v (52/100*100v)

=> loser obtained (total - non cast - winner's) 100v-8v-52v=40v

difference in votes in terms of v = 52v-40v=12v

actual difference=120

=> 12v=120

=> v= 120/12 = 10

WINNER got 52v votes = 52*10= 520 votes.