Last year, all registered voters in Kumannia voted either for the Revo

Question

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?

A. 5/18
B. 7/18
C. 1/2
D. 5/9
E. 11/18

A. 5/18
B. 7/18
C. 1/2
D. 5/9
E. 11/18

Bunuel · Accepted Answer

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.

adamsmith2010 · Answer

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?

xcusemeplz2009 · Answer

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

umaa · Answer

Even I've got 60%. But the answer is 11/18.

DestinyChild · Answer

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

Jinglander · Answer

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.

jakolik · Answer

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

crack700 · Answer

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

cano · Answer

Yes, 1.1/1.8 = 11/18

FullFathomFive · Answer

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!

jlgdr · Answer

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

mniyer · Answer

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 · Answer

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 .

BrainLab · Answer

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

lalania1 · Answer

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

LeenaSai · Answer

Hi chetan2u @ Bunuel I am unable to get the answer for this question

As per my understanding , S —————————————R 105 108 110 3 : 2 So , the relation between the no. of voters who voted for the respective party wrt the total number of voters is , 2:3 So , the fraction of R party voters will be 3/5 Plz provide your insight plz Posted from my mobile device

Kritisood · Answer

i took me 4 mins to solve it but after i did, it seems pretty easy
let the number of voters of Revolutionary be r and Status Que be s

r=3/2s (see bunuels explantion)

now we need to find 110r/108(r+s) 
110r = R's voters this yr after the increase
108(r+s) = total this year after the increase

put r=3/2s in this
110*3/2s=55*3*S
108(r+s) = 54*5*S

55*3*S/54*5*S=11/18

KarishmaB · Answer

Responding to a pm:

Yes, you can solve it using weighted avgs.

w1/w2 = (5 - 8)/(8 - 10) = 3/2 
Ratio of initial voters for Rev/Status = 3/2 (Note that since we are averaging increase, the weights will be the initial ratio of voters in the two camps)

So for 100 voters, 60 voted Rev and 40 voted Status.
Number of Rev increased this year by 10% so became 66.
Total number increased by 8% so became 108 this year.

Fraction of voters who voted Rev this year = 66/108 = 11/18

Answer (E)

Archit3110 · Answer

let total votes ; 50
given
previous year ; x+y =50
and this year ; 1.1x+1.05y = 54
solve for x & y we get last year x= 30 and y = 20 
and this year x= 33 and y = 21
so fraction of voters voted Revolutionary this year ; 33/54 ; 11/18
OPTION E

Last year, all registered voters in Kumannia voted either for the Revo

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