Thursday, July 30, 2009

General election problem?

here i have uploaded a problem image


http://i218.photobucket.com/albums/cc298...





please zoom the image to see it more clearly.





this is how United nation's secretary general is elected.





did you see the table ?





can we say the Total votes in round-1 ? How ?





i also see in round-1 A has got 60 (so,A is the max vote winner..right?) and D has got the least votes 24.(D is lowest...right?)





can we find number of votes cast for C in round-1 ?

General election problem?
There were 164 votes in round one. D's country lost its vote (for D by (vi)) when D was eliminated in round one.





Vote totals for round one:





A: 60


B: 80 - x


C: x


D: 24





with x at least 25.





Now to round two: There were three candidates and 163 votes.





A: 163 - 64 - 39 = 60


B: 64


C: 39





C was eliminated. C's country lost its vote for round three, as did any country voting for D in round one, and then C in round two, by (i). The total lost was 163-147 = 16, so 15 voted D in round one and C in round two. Then C had 39-15 = 24 holdover votes from round one, by (ii). That also means the other 8 (24-1-15) votes for D in round one went to B in round two.





Now, nobody that voted for C in round one switched to A in round two by (ii) and the fact A still has 60 votes. So, the 24 holdovers are the remaining 75% of x, the other 25% going to B.





Then 24 = (75%)x=(75/100)x means 32 = 24(100/75) = x.





C had 32 votes in round 1, and B had 80-32 = 48.





Now to round three.





32/2 = 16 total votes for C in round one went to B in round three. 8 already defected as of round two. Thus B will get 64+8 = 72 votes in round three. A will get the rest, 147-72=75. So A is the come-from-behind winner.


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