Question

In an election contest 10% of enlisted voters did not cast their votes and 600 of the votes cast were cancelled. The winner won by a margin of 4080 votes by securing votes from 47% of the enlisted voters. Find the total number of enlisted voters and number of votes secured by loser candidate ?

Answer 1

Let the votes received by winner and looser be W and L.

And, total number enlisted voters be V.

Given -

10 % of the enlisted voters did not cast their votes.

600 of the votes were cancelled.

Winning margin = 4080 votes by securing 47 % of the enlisted voters.

Now according to the question.

⇒ W + L = 0.9V - 600 ..............(1)

⇒ W - L = 4080  .......................(2)

Adding both equations

     W + L = 0.9V - 600
     W - L =           4080
    ________________
    2W    = 0.9V + 3480
   _________________

As the winner got 47 % votes of the total enlisted voters.

Therefore, 2*0.47V = 0.9V + 3480

⇒ 0.94V - 0.9V = 3480

⇒ 0.04V = 3480

⇒ V = 3480/0.04

⇒ V = 87000

So, total number of enlisted votes are 87000

Votes received by the winner = (87000*47)/100

= 40890

Votes received by the looser = 87000 - (10 % of 87000 + 600 + 40890)

⇒ 87000 - (8700 + 600 + 40890)

⇒ 87000 - 50190

= 36810

So, looser secured 36810 votes.

Answer.