Let be the total members of the society voted for . Let denote the number of candidates voted for respectively. Then,
Adding (4) and (5), we get
Subtracting (8) from (7), we get .
From (4), (5), (6)
ii) Number of candidates who did not vote =
iii) Number of members voted for X only =
iv) Number of votes for X only = 76,
Number of votes for Y only = 59,
Number of votes for Z only = 37.
Therefore, X won the election.