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# Of the votes cast on a certain proposal, 80 more were in favor of the

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Math Expert
Joined: 02 Sep 2009
Posts: 44599
Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink]

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24 Nov 2015, 10:31
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:25) correct 20% (01:51) wrong based on 70 sessions

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Of the votes cast on a certain proposal, 80 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)

(A) 480
(B) 400
(C) 300
(D) 240
(E) 160
[Reveal] Spoiler: OA

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Joined: 10 Aug 2015
Posts: 103
Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink]

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24 Nov 2015, 10:43
Bunuel wrote:
Of the votes cast on a certain proposal, 80 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)

(A) 480
(B) 400
(C) 300
(D) 240
(E) 160

Solution : Let x be no. of votes against the proposal. Then no. of votes in favor would be x+80 and total no. of votes would be 2x+80.
40%(2X + 80) = X ==> X=160.
Total no. of votes = 2(160) + 80 = 400

Option B
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink]

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24 Nov 2015, 10:48
Let the total number of votes cast = T
Number of votes cast in favour of proposal = F
Number of votes cast against the proposal = A

F = A + 80 -- 1
Since , the number of votes against the proposal was 40 percent of the total vote
A= (40/100)*T = .4T -- 2
=> F = (60/100)*T = .6T -- 3

From equations 1 , 2 and 3 ,we get
.2T = 80
=> T= 400
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink]

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07 Dec 2015, 17:50
Let x be the total of votes cast, the solution we want.
Number of people against the proposal: $$\frac{40}{100}$$ x
Number of people in favor: 1 - $$\frac{40}{100}$$ x = $$\frac{60}{100}$$ x

Since,
Bunuel wrote:
80 more were in favor of the proposal than were against it

that means 80 is the difference of the two percentages.
$$\frac{60}{100}$$ x - $$\frac{40}{100}$$ x = $$\frac{20}{100}$$ x

$$\frac{20}{100}$$ x = 80
x = 400
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink]

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08 Dec 2015, 01:14
favour of proposal =x+80
against the proposal=x
now,
.4(2x+80)=x
.8x+32=x
.2x=320
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink]

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08 Dec 2015, 17:54
Hi All,

This question can be solved by TESTing THE ANSWERS.

Under normal circumstances, we would start by TESTing Answer B or D first. Since B is the 'easier' value, we'll start there...

We're told that 40% of the total votes were votes AGAINST the proposal:

So the remaining votes were in FAVOR of the proposal:
400 - 160 = 240 votes for

With these two numbers, the difference is 240-160 = 80, which is a MATCH for what we were told. Thus, this MUST be the answer.

[Reveal] Spoiler:
B

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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink]

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09 Jan 2016, 02:36
Against = x
For = x+80

get proportion

x/x+x+80=4/10

10x=8x+320 => x=160, so total number = 160*2+80=400

B
Math Expert
Joined: 02 Aug 2009
Posts: 5774
Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink]

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09 Jan 2016, 03:16
1
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Expert's post
Bunuel wrote:
Of the votes cast on a certain proposal, 80 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)

(A) 480
(B) 400
(C) 300
(D) 240
(E) 160

Hi,
Although a relatively simpler Question, fast thinking can save time for slightly complex Qs later..
the difference is 20% which is given as 80..
so total will be 80/20 * 100=400
B
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the [#permalink]

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13 Dec 2017, 07:30
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Re: Of the votes cast on a certain proposal, 80 more were in favor of the   [#permalink] 13 Dec 2017, 07:30
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