An election was held between two persons to select a representative to a certain institution. All the voters who were registered cast their votes. The winner
received 7/12 of the votes and
won by a majority of 120 votes.

(i) What fraction of the total votes did the person who lost receive?
(ii) How many registered voters were there?
(iii) Find the number of votes the winner received.​

9514 1404 393

  (i)  5/12

  (ii)  720

  (iii)  420

Step-by-step explanation:

(i) The fraction representing all votes is 12/12. If 7/12 were received by the winner, then the loser received 12/12 -7/12 = 5/12 of the total votes.

  The person who lost received 5/12 of the total votes.

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(ii) The winner won by 7/12 -5/12 = 2/12 = 1/6 of all votes. So, the total number of votes is ...

  120 votes = 1/6(total votes)

  total votes = 6×120 votes = 720 votes

There were 720 registered voters.

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(iii) The winner received ...

  (7/12)(720 votes) = 420 votes . . . received by the winner