The population of a city vote for one among 4 political parties, A, B

Can you help me understand how did you arrive at this solution?

How did you get 40? 8 and 10 came from where?

Posted from my mobile device

\(A+B+C+D+F(Fluctuate)=100\)
\(A+25+25+10+10=100\)
\((AM+AF)+(BM+BF)+(CM+CF)+(DM+DF)+10=100\)
\(AF+BF+CF+DF+F'=50 and AM+BM+CM+DM+F''=50, (F'+F''=10)\)
\(DF=5, DM=5,F'=5, F''=5, BF=0, CM=0\)
\(AF+0+25+5+5=50\)
\(AF=15\)
\(AM+25+0+5+5=50\)
\(AM=15\)
\(A= 30\)
But male voters except those who fluctuate= 15-5=10
male % won by A=\(10/30\)
33.33
D:)

Could you please explain why did you subtract 5 from the male voters since the count of 15 already had no fluctuating voters, even i followed the same approach and got the same number except the final answer. Since the question tells to remove the fluctuating voters i found the probability using 15/90 instead it should have been 15/30 where m i going wrong?

Posted from my mobile device

We can let the total number of voters be 200 (100 male and 100 female). So 50 voters (all of whom are male) are committed to party B, 50 voters (all of whom are female) to party C, and 20 voters (10 male and 10 female) to party D, leaving 20 voters (10 male and 10 female) to fluctuate. Thus, the remaining 30 male and 30 female voters are committed to party A. Since 90 male voters (all except the 10 who fluctuate) will cast their votes, 30/90 = 1/3 = 33.33% of the male votes will be won by party A.

Answer: D

Male Female Total
A 15 15 30
B 25 0 25
C 0 25 25
D 5 5 10
Non 5 5 10
100

Hence total male percent =\( \frac{15}{45}*100\)
thus 33.3%
D

Why the 5 male voters who fluctuate should not be included?

The stimulus says clearly "what percent of the male votes will be won by party A"

Hi jcgomezlv,

The question statement clearly states that the voters who fluctuate DID NOT vote.
Since, they did not vote, we cannot possibly count them in.
Hence, we explicitly subtract 5 from the total number of male voters (50) and this gives us the total number of male voters = 45

Hope that helps!

porwal1

satya2029 is incorrect in the final piece of logic, and you are correct. We do not need to subtract 5 from 15. Rather we need to subtract 5 from 50.

Total male voters - Fluctuating male voters = 50 - 5 = 45

Total Male A / Total Male who will actually vote = 15 / 45 = 33.33%