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In an election between two candidates, the winner has a marg

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b2bt
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In an election between two candidates, the winner has a marg [#permalink] New post   24 Sep 2013, 23:16
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In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?

a. 30,000
b. 15,450
c. 45,000
d. 60,000
e. 15,000
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E
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mau5
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Re: In an election between two candidates, the winner has a marg [#permalink] New post   24 Sep 2013, 23:32
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b2bt wrote:
In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?

a. 30,000
b. 15,450
c. 45,000
d. 60,000
e. 15,000


Total # of votes cast = 100x, out of these, let the # of votes won by the winner = w, and for the loser(l) = 100x-w. Given that w-(100x-w) = 10% of total votes cast = 10x

Thus, 2w-100x = 10x \(\to\) w = 55x and l = 100x-55x = 45x.

According to the new condition, if the loser had won 45x+1500 votes, then , (45x+1500)-(55x-1500) = 10 % of total votes cast = 10x

Thus, 3000 = 20x and 100x = 15000.

E.
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Re: In an election between two candidates, the winner has a marg [#permalink] New post   25 Sep 2013, 02:03
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b2bt wrote:
In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?

a. 30,000
b. 15,450
c. 45,000
d. 60,000
e. 15,000


Winner - Looser
55% - 45%

If 1500 people change their mind and vote for the loser:
Winner - Looser
45% - 55%

Thus 1,500 people compose 10% of all voters, which means that the total number of votes is 15,000.

Answer: E.
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Re: In an election between two candidates, the winner has a marg [#permalink] New post   25 Sep 2013, 02:28
Condition 1 : W-L=0.1V

Condition 2: L+1500-(W-1500) = 0.1V

So, V=15000

Hence, E :)
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Re: In an election between two candidates, the winner has a marg [#permalink] New post   25 Sep 2013, 09:56
Bunuel wrote:
b2bt wrote:
In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?

a. 30,000
b. 15,450
c. 45,000
d. 60,000
e. 15,000


Winner - Looser
55% - 45%

If 1500 people change their mind and vote for the loser:
Winner - Looser
45% - 55%

Thus 1,500 people compose 10% of all voters, which means that the total number of votes is 15,000.

Answer: E.



Hi Bunuel, How are we concluding 55-45 here?
I took it as 60-40 and messed up but however got the answer right.

I want to know how "logically" we can conclude it (55-45)
mau5 method is too alegbric for me :) :P
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Bunuel
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Re: In an election between two candidates, the winner has a marg [#permalink] New post   25 Sep 2013, 09:58
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b2bt wrote:
Bunuel wrote:
b2bt wrote:
In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?

a. 30,000
b. 15,450
c. 45,000
d. 60,000
e. 15,000


Winner - Looser
55% - 45%

If 1500 people change their mind and vote for the loser:
Winner - Looser
45% - 55%

Thus 1,500 people compose 10% of all voters, which means that the total number of votes is 15,000.

Answer: E.



Hi Bunuel, How are we concluding 55-45 here?
I took it as 60-40 and messed up but however got the answer right.

I want to know how "logically" we can conclude it (55-45)
mau5 method is too alegbric for me :) :P


The winner has a margin of 10% of the votes polled --> x+(x+10)=100 --> x=45 and x+10=55.
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Re: In an election between two candidates, the winner has a marg [#permalink] New post   03 Jun 2016, 10:51
b2bt wrote:
In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled.Find the total number of votes polled in the election?

a. 30,000
b. 15,450
c. 45,000
d. 60,000
e. 15,000


Attachment:
Voters.PNG
Voters.PNG [ 3.03 KiB | Viewed 7678 times ]


So, 10--------->1500
Or, 100-------->15000

Hence correct answer will be (E)
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Re: In an election between two candidates, the winner has a marg [#permalink] New post   17 Aug 2023, 23:21
In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?

Let the total no. of votes be 2x

In Case 1:-
The winner got 110% of (2x/2) = 1.1x
Therefore loser get 2x-1.1x=0.9x

In Case 2:-
0.9x + 1500 = 1.1x
=>0.2x = 1500
=> x =7500

The no. of votes =2x=2*7500=15000

Hence E
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Re: In an election between two candidates, the winner has a marg [#permalink]
17 Aug 2023, 23:21
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