In a survay 80 students were asked if they liked vanolla or chocolate cake 35 students liked vanilla 32students liked chocolate 24 students said they didn't liked either How many students liked both vanilla and chocolate

67 students liked both vanilla and chocolate

108,913 people vote for other candidates

In this case, you know the total number of winning voters and the vote differences between two candidates. Then the Winning (W) and Losing(L) candidate equation would be :
W= 138,201
W-L = 29,288 

If you put the first equation into the second, you will get
W-L = 29,288 
138,201-L= 29,288 
-L= 29,288 - 138,201
-L= -108,913
L= 108,913