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Thank you!

So for the split of 90, i need to look at it as 60:30 for 2:1 ratio. Thanks again!
Bunuel


Your error is that you treated the 15 in-favor votes as fixed. They are not fixed because the remaining votes will add more in-favor votes too. So you cannot scale 5 up to 30. That step is the mistake. Please review the previous two pages of the discussion for more.
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hi Bunuel,
I am not sure where i am wrong, please correct me

I took the total number to be 3600
2/9th is 800 and 600 is for and 200 is against; the remaining is 3600-800 gives 2800
to get 2:1 against,
the against should be 1200 as the for is 600
we already have 200, so the remaining 1000 should be from the 2800 remaining
1000/2800 gives me 5/14 and not 11/14

Please find my error

Thanks in advance,
Swetha
Bunuel


If we use a variable for the total number of votes, there will be too many fractions to manipulate. So, let's choose a smart number: set the total number of votes at 18.

"2/9 of the votes on a certain resolution have been counted" means 4 votes are counted, and 18 - 4 = 14 votes yet to be counted.
"3/4 of those counted are in favor of the resolution" means 3 votes are in favor and 1 against.

For the ratio of those who voted against to those who voted for to be 2 to 1, there should be a total of 18*2/3 = 12 people who voted against. Therefore, in the remaining 14 votes, there should be 12 - 1 = 11 people who voted against. Hence, 11/14 of the remaining votes must be against.

Answer: A.
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SwethaReddyL
hi Bunuel,
I am not sure where i am wrong, please correct me

I took the total number to be 3600
2/9th is 800 and 600 is for and 200 is against; the remaining is 3600-800 gives 2800
to get 2:1 against,
the against should be 1200 as the for is 600
we already have 200, so the remaining 1000 should be from the 2800 remaining
1000/2800 gives me 5/14 and not 11/14

Please find my error

Thanks in advance,
Swetha

Your mistake is in this line:

“the against should be 1200 as the for is 600”

That 600 “for” is only among the first 800 counted votes, not the final total. The final total must be 2 to 1 against, so out of 3600 votes the final counts must be:
against = 2400 and for = 1200.

You already have against = 200 from the first batch, so the remaining against votes must be 2400 - 200 = 2200 out of the remaining 2800 votes.

That fraction is 2200/2800 = 11/14.

Hope it's clear.
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here is the solution based on what i have understood by reading

it says 2/9 is the total votes which have been done out of the total number of votes which are 1; votes remaining are (1-2/9) = "7/9"

now 3/4th of the 2/9 votes are in favour which means that 1/4th of the 2/9 votes are not in favour or against.

so in favor = 3/4*2/9 = 1/6 of total votes
against = 1/4*2/9 = 1/18 of total votes


Similarly in the remaining number of votes which will be 7/9 some portion is in favor some is in against lets say x fraction is in favor which means (1-x) is in against.

therefore, 7/9*x and 7/9(1-x) respectively

now it says total vote against = 2* total vote in favor; substitute the values

7/9(1-x) + 1/18 = 7/9x + 1/36,

upon solving this we will get x = 3/14; but we want the fraction votes against which is 1-x = 1-3/14

= 11/14 Ans
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