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 5%. No other votes were cast.
If the number of total voters increased 8%, what fraction of voters voted Revolutionary
this year?
Source-MGMAT Guide 1
Am trying to solve this through allegations:

5%(S)_________8%______10%(R)

So,5%(S)____2x____8%___3x___10%(R)

R/Total=3/5*100=60%
But correct ans is 61.1
Someone please guide me where am i making a mistake.

arpshriv wrote:...what fraction of voters voted Revolutionary this year?

According to your solution, you have determined the ratio of R to (S + R), where S and R are number of voters for Status Quo and Revolutionary party for the last year. But the problem asked for the ratio for this year.

This year number of voters for Revolutionary party = R + 10% of R = 1.10*R
And, number of total voters = (R + S) + 8% of (R + S) = 1.08*(R + S)

So, required ratio = (1.10*R)/(1.08*(R + S)) = (1.10/1.08)*(R/(S + R)) = (1.10/1.08)*(3/5) = (55/54)*(3/5) = 11/18

Aishwarya1204 wrote:Last year all registered voters either voted for the Revolutionary party or the Status Quo party. This year the number of revolutionary voters increased by 10% and the Status Quo voters increased by 5%. No other votes were cast. If the number of total votes increased by 8%. What fraction of voters voted for the Revolutionary party this year.

Answer is [spoiler] 11/18 [/spoiler]

This is a WEIGHTED AVERAGE/MIXTURE problem.
Let R = Revolutionary voters and S = Status Quo voters.
Increase in R = 10%.
Increase in S = 5%.
Increase in the MIXTURE of R+S = 8%.

To determine the ratio of R to S in the mixture, use ALLIGATION.

Step 1: Plot the 3 percentages on a number line, with the percentage increases for R and S (10% and 5%) on the ends and the percentage increase for the mixture (8%) in the middle.
R (10%)------------8%------------(5%) S

Step 2: Calculate the distances between the percentages.
R (10%)-----2-----8%-----3-----(5%) S

Step 3: Determine the ratio in the mixture.
The required ratio of R to S is equal to the RECIPROCAL of the distances in red:
R:S = 3:2.

The result implies that LAST YEAR -- before the 10% increase in R and the 5% increase in S -- there were 3 R voters for every 2 S voters.

To determine R:S THIS YEAR, plug in values for R and S.
Let R last year = 30 and S last year = 20.
This year:
R increased by 10% = (1.1)*30 = 33.
S increased by 5% = (1.05)*20 = 21.
R/(R+S) = 33/(33+21) = 33/54 = 11/18.

For more practice will alligation, check here:
https://www.beatthegmat.com/ratios-fract ... 15365.html