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Intern  Joined: 16 Jun 2008
Posts: 5
Last year, all registered voters in Kumannia voted either  [#permalink]

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4
15 00:00

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(N/A)

Question Stats: 38% (03:09) correct 62% (03:37) wrong based on 51 sessions

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Last year, all registered voters in Kumannia voted either for the Revolutionary Party or for the Status Quo Party. This year, the number of revolutionary voters increased 10%, while the number of Status Que voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?
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Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: Kumannia  [#permalink]

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10
10
umaa wrote:
Last year, all registered voters in Kumannia voted either for the Revolutionary Party or for the Status Quo Party. This year, the number of revolutionary voters increased 10%, while the number of Status Que voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?

Set the equation for the number of total voters this year: $$1.1R+1.05S=1.08(R+S)$$ --> $$2R=3S$$

The question is $$\frac{1.1R}{1.1R+1.05S}=?$$ --> $$\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}$$. Now, as $$2R=3S$$ then $$70R=105S$$ (multiplying by 35) --> substitute 105S by 70R: $$\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}$$

Hope it's clear.
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Intern  Joined: 17 Dec 2009
Posts: 24
Re: Kumannia  [#permalink]

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Can you use the alligation method here?

If voters of the Revolutionary party increased 10% and the Status Quo Party increased 5% and the overall total votes increased 8% then the Revolutionary party accounted for 60% of the vote.

R-------Average--------S
+10 +8 +5
(2 away from mean) (3 away from mean)
So

R/(R+S) = (3/5) or 60%.

Is this correct?

Originally posted by adamsmith2010 on 17 Dec 2009, 16:05.
Last edited by adamsmith2010 on 18 Dec 2009, 08:26, edited 1 time in total.
Manager  Joined: 09 May 2009
Posts: 176
Re: Kumannia  [#permalink]

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revolutionary voter=r
status quo voter=s
total=t
t=r+s---->s=t-r

new r=1.1r
new s=1.05s
new t=1.08 t
---->1.1r+1.05s=1.08t
--->1.1r+1.05(t-r)=1.08t
--->.05r=.03t
---->r=3/5t

OA pls
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Intern  Joined: 16 Jun 2008
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Re: Kumannia  [#permalink]

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Even I've got 60%. But the answer is 11/18.
Manager  Joined: 02 Oct 2009
Posts: 163
Re: Kumannia  [#permalink]

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1
11/18

1.1x+1.05y=1.08(x+y)
.02x=.03y
2x=3y (thought just it out there for more visually charged people like me).

1.1x/1.1x+1.05(2/3)x
(after drowning with decimals)

11/18
Manager  Joined: 24 May 2010
Posts: 75
Percents and voters  [#permalink]

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Last year all the voters of a country voted for party A or party B. This year the number of voters voiting for A increased by 10% while the voters for party B increased by 5%. If the total number of voters increased by 8% what fraction of voters voted for party A this year.
Manager  Joined: 16 Apr 2010
Posts: 197
Re: Percents and voters  [#permalink]

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Hi,

Let x be the percentage that voted for A and (100-x) the percentage who voted for B.

we have 1.1x + 1.05(100-x) = 8
Solving for x we get x = 60 (who voted for A) and (100-60) who voted for B.

regards,
Jack
Manager  Joined: 20 Mar 2010
Posts: 77
Re: Percents and voters  [#permalink]

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1
Jinglander wrote:
Last year all the voters of a country voted for party A or party B. This year the number of voters voiting for A increased by 10% while the voters for party B increased by 5%. If the total number of voters increased by 8% what fraction of voters voted for party A this year.

Let a be the number of voters who voted for party A and be the number of voters who voted for party B last year.
Party A | Party B
--------------------------
a | b <---- Last yr
1.1 a | 1.05 b <-----This yr

The question also states that the total voters increased by 8% this year. So
1.1a + 1.05b = 1.08(a+b) => b =(2/3)*a

We need to find the fraction of voters who voted for party A this year i.e 1.1a/(1.1a + 1.05b)
= 1.1a/(1.1a + 1.05*(2/3)*a) = 1.1/1.8 =11/18
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Re: Kumannia  [#permalink]

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Yes, 1.1/1.8 = 11/18
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Re: Kumannia  [#permalink]

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Bunuel wrote:
umaa wrote:
Last year, all registered voters in Kumannia voted either for the Revolutionary Party or for the Status Quo Party. This year, the number of revolutionary voters increased 10%, while the number of Status Que voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?

Set the equation for the number of total voters this year: $$1.1R+1.05S=1.08(R+S)$$ --> $$2R=3S$$

The question is $$\frac{1.1R}{1.1R+1.05S}=?$$ --> $$\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}$$. Now, as $$2R=3S$$ then $$70R=105S$$ (multiplying by 35) --> substitute 105S by 70R: $$\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}$$

Hope it's clear.

I wish I could Kudos Bunuel's explanation a thousand times. I have found MGMAT's explanation of this problem, with their whole chart approach, almost indecipherable. Thank you for the clarity Bunuel!
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Re: Kumannia  [#permalink]

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Bunuel wrote:
umaa wrote:
Last year, all registered voters in Kumannia voted either for the Revolutionary Party or for the Status Quo Party. This year, the number of revolutionary voters increased 10%, while the number of Status Que voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?

Set the equation for the number of total voters this year: $$1.1R+1.05S=1.08(R+S)$$ --> $$2R=3S$$

The question is $$\frac{1.1R}{1.1R+1.05S}=?$$ --> $$\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}$$. Now, as $$2R=3S$$ then $$70R=105S$$ (multiplying by 35) --> substitute 105S by 70R: $$\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}$$

Hope it's clear.

Yeah, I'm afraid I made the same mistake by using differentials we only find the ratio of votes for LAST YEAR, we are being asked something else.
Agree with method by Bunuel to solve this. I think more than one got caught with the 60%

Cheers!
J Intern  Joined: 06 Apr 2011
Posts: 41
Re: Kumannia  [#permalink]

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Hi Bunuel,
I have a clarification though...

After we get 2R = 3S as the equation for the total voters this year, doesn't this imply R/S = 3/2 and therefore R/(R+S) = 3/5? (After all, we derived 2R = 3S considering the voters increased 10% and 5% respectively this year?)

Appreciate any explanation.

Bunuel wrote:

Set the equation for the number of total voters this year: $$1.1R+1.05S=1.08(R+S)$$ --> $$2R=3S$$

The question is $$\frac{1.1R}{1.1R+1.05S}=?$$ --> $$\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}$$. Now, as $$2R=3S$$ then $$70R=105S$$ (multiplying by 35) --> substitute 105S by 70R: $$\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}$$

Hope it's clear.
Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: Kumannia  [#permalink]

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mniyer wrote:
Hi Bunuel,
I have a clarification though...

After we get 2R = 3S as the equation for the total voters this year, doesn't this imply R/S = 3/2 and therefore R/(R+S) = 3/5? (After all, we derived 2R = 3S considering the voters increased 10% and 5% respectively this year?)

Appreciate any explanation.

Bunuel wrote:

Set the equation for the number of total voters this year: $$1.1R+1.05S=1.08(R+S)$$ --> $$2R=3S$$

The question is $$\frac{1.1R}{1.1R+1.05S}=?$$ --> $$\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}$$. Now, as $$2R=3S$$ then $$70R=105S$$ (multiplying by 35) --> substitute 105S by 70R: $$\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}$$

Hope it's clear.

Yes, from $$2R=3S$$ we get R/(R+S)=3/5, but notice that R and S there denote the number of voters last year.
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Last year, all registered voters in Kumannia voted either  [#permalink]

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1
mniyer wrote:
Hi Bunuel,
I have a clarification though...

After we get 2R = 3S as the equation for the total voters this year, doesn't this imply R/S = 3/2 and therefore R/(R+S) = 3/5? (After all, we derived 2R = 3S considering the voters increased 10% and 5% respectively this year?)

Appreciate any explanation.

Bunuel wrote:

Set the equation for the number of total voters this year: $$1.1R+1.05S=1.08(R+S)$$ --> $$2R=3S$$

The question is $$\frac{1.1R}{1.1R+1.05S}=?$$ --> $$\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}$$. Now, as $$2R=3S$$ then $$70R=105S$$ (multiplying by 35) --> substitute 105S by 70R: $$\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}$$

Hope it's clear.

As Bunuel already stated R/Total = 3/5 is a ration for the last year, for this year yoiu must do the following:
Revolutionary voters: 3+10% Increase = $$3+\frac{3}{10}=\frac{33}{10}$$
Total: 5 + 8% Increase = 5+0,4 = $$\frac{54}{10}$$
So the fraction for this year is equal to $$\frac{33}{10}:\frac{54}{10}$$ = $$\frac{33}{10}*\frac{10}{54}=\frac{11}{18}$$
Hopoe it's clear now
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Manager  Joined: 17 Nov 2013
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Re: Last year, all registered voters in Kumannia voted either  [#permalink]

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110X + 105Y = 108 (X+Y)
2X = 3Y

the question is:
110x/110x + 105y =?

if 2x = 3y => 70x = 105y when multiplied by 35.

then, 110x/(110x + 70x) = 110x/180x = 11/18
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Re: Last year, all registered voters in Kumannia voted either  [#permalink]

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_________________ Re: Last year, all registered voters in Kumannia voted either   [#permalink] 06 Aug 2018, 11:07
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