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?

I don't understand MGMAT strategy guide explanation. I used another formula and I got the answer 60%.

1.1R + 1.05 Q/(R+Q) = 1.08

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_________________
Ben Ku
Instructor
ManhattanGMAT

its from MGMAT fractions book ( 3rd edition) chapter # 3
page # 66

Kindly help me how to do it as per the alligation method.

Thanks

Bhumika

What is the Alligator Method?

The approach given in the Strategy Guide's explanations uses the smart number 100 to represent last year's Revolutionary voters. Another algebraic approach is to assign R as the number of Revolutionary voters last year and T to be the total voters last year.

R = Revolutionary voters last year
T - R = Status Quo voters last year
T = Total voters last year

So for this year, the number of Revolutionary voters increased 10%, number of Status Quo voters increased 5%, and Total voters increased 8%. So

1.10 R = Revolutionary voters this year
1.05 (T - R) = Status Quo voters this year
1.08 T = Total voters this year.

Because the number of Revolutionary voters and Status Quo voters is equal to the total voters this year, we set up the following equation.

1.10R + 1.05(T - R) = 1.08 T
1.10R + 1.05T - 1.05R = 1.08T
0.05R = 0.03T
R/T = 3/5

We are looking for the fraction of Revolutionary voters this year, so we need the fraction 1.10R / 1.08T. We can do this by multiplying the ratio above by 1.10/1.08.

1.10R / 1.08T = (3/5)(1.10/1.08) = 11/18

Hope that makes sense.

_________________
Ben Ku
Instructor
ManhattanGMAT