Problem Solving

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 Quo voters increased S%. No other votes were cast. If the number of
total voters increased 8%, what fraction of voters voted Revolutionary this year?

OA [spoiler]11/18[/spoiler]

Assume there were R voters for the Revolutionary party and S voters for the Status Quo party last year. We have R + S = total voters.

Given the increases stated there would be 1.10*R and 1.05*S for the respective parties this year and 1.08*(R+S) total voters. (Assuming the increase in party S is 5%, the question looks as though it might be S%.)

So we can set these equal: 1.10*R + 1.05*S = 1.08 *(R+S) Simplifying we get .02R = .03S. that makes the ratio of R:S = 3:2.

Assume there were 100 voters last year. That means there were 60 voters for R and 40 for S. Applying our increases we get this year's totals at 66 for R and 42 for S (total 108).

We are looking for the fraction of voters voting for party R. That is 66/108 or 11/18.

I posted an alternate solution here:

https://www.beatthegmat.com/fdp-problem- ... tml#347379