Last year, all registered voters in Kumannia voted either

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?

according to alligation rule:q1/q2=c2-cm/cm-c1. 
c2(revolution)=10,c1(status)=5,cm(voters)=8
therefore, revolutionary/status quo=10-8/8-5=2/3.
fraction of voters voted Revolutionary this year=2/5=.40 
where i went wrong,pls explain 
 11/18

Bunuel · Answer

Here is another approach maybe you find it easier:
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.

LalaB · Answer

please pay attention, that u are asked the fraction of these guys AFTER the increase in fact, u were on a right way 1.1R+1.05Q=1.08(R+Q) 2R=3Q till here everything was ok with ur solution 2R=3Q means R/Q=3/2 it means that R=3/5*TOTAL now u need to find our the fraction of all these guys after increase lets assume that total was 5 , then R was 3 after increase (3+10%)/(5+8%)=3.3/5.4=33/54=11/18 hope I could be helpful

TomB · Answer

thank you guys. got it

subhajeet · Answer

Let voters for revolutionary party be a and that for the status quo party be b 
so this year voters for revolutionary party be a+a/10 and for status quo party be b+5b/100
and the increase in the voters be (a+b)+(a+b)8/100 ................(1)
so (a+b)+(a+b)8/100 = a+a/10 + b+5b/100
on solving we get 3b=2a
put this in eq (1) and we get the value as 18a/10
so the fraction is (11a/10)/(18a/10) =11/18

iaratul · Answer

I am having real trouble with these questions. The Manhattan GMAT Strategy Guide is providing a good way to solve this, with the chart - and I'm understanding the solutions very well. But the trouble is, when I see a similar problem, I'm getting stuck because I can't seem to reinitiate similar logic for that question. Although I'm just starting up, I need to know if there is a simpler logic-flow I can follow and I will understand the moment I see it. Can anyone help me with this?

JapinderKaur · Answer

Dear Iaratul

My suggestion would be to try constructing equations directly from the word problem, whenever you feel puzzled about how to fit the alligation chart in the given scenario. These equations are pretty easy to write.

Let me illustrate what I mean with a sample question.

Question: A box contains a mixture of coffee powder and sugar. Adding 20% more coffee and 30% more sugar to the box increases the weight of the box by 25%. What is the current ratio of coffee powder and sugar in the box?

Solution:

We will solve this through the equation method.

Let the amount of coffee initially = c
Amount of sugar initially = s
So, initial weight of the box = c+s (discounting the weight of the material from which the box is made, since it remains constant throughout the question)

Now, how much coffee was added? 20% of c.
So, what will be the final amount of coffee? c+20% of c = 1.2c
Similarly, the final amount of sugar = 1.3 s

After adding both these things, when the weight of the box was measured, it came to be 25% more than before.

So, new weight = 1.25(old weight) = 1.25(c+s)

Now,

New weight of the box = New weight of coffee + New weight of sugar

1.25(c+s) = 1.2c + 1.3s

Solving these, we get, c=s

So,

\frac{Current Ratio of Coffee}{Current Ratio of Sugar}   =\frac{1.2c}{1.3s}  =\frac{12}{13}

Hope I could help!

KarishmaB · Answer

Check out the blog posts on the link given in my signature below.

PareshGmat · Answer

Revol............... Status Quo.............. Total

x ................... 100-x ...................... 100 (assumed)

10% increase in Revol; 5% increase in Status Quo; Total increase = 8%

New values as below

x+\frac{10x}{100} ......... 100-x + \frac{5(100-x)}{100} ............ 108

Solving the equation as below:

\frac{110x}{100} + \frac{10500-105x}{100} = 108

x = 60

\frac{110x}{100} = 66 = Votes obtained by Revol this year

108 = Total votes polled this year

Ratio = \frac{66}{108} = \frac{11}{18}

ronr34 · Answer

Hi Karishma.
I went over the link you gave here, but am still having problems implementing this correctly.
I tried the scale method and got a 2/3 ration but I don't see how to move on from here.
Can you help?

KarishmaB · Answer

What is 2/3 that you obtained? It is the original ratio of Status Quo/Revolutionary. So total voters on the ratio scale is 5.

What you need is "what fraction of voters voted Revolutionary  this year ?"

This year, revolutionary voters increased 10% 
Revolutionary voters = 3*(1.1) 
Total voters = 5*(1.08)

Fraction of Revolutionary voters  = \frac{3*1.1}{5*1.08} = \frac{11}{18}

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Last year, all registered voters in Kumannia voted either

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Last year, all registered voters in Kumannia voted either

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards