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15 Dec 2021, 08:23
Kudos
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Given: 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.
Asked: If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?
Last year: -
Let the Number of voters who voted for Revolutionary Party = r
Let the Number of voters who voted for Status Quo Party = s
Total voters who voted = r + s
This year: -
The Number of voters who voted for Revolutionary Party =1.1r
The Number of voters who voted for Status Quo Party = 1.05s
Total voters who voted = 1.1r + 1.05s = 1.08(r+s)
.02r = .03s
r = 1.5s
The Number of voters who voted for Revolutionary Party =1.1r = 1.1*1.5s = 1.65s
The Number of voters who voted for Status Quo Party = 1.05s
Total voters who voted = 1.65s + 1.05s = 2.7s
The fraction of voters voted Revolutionary this year = 1.65s / 2.7s = 165/270 = 11/18
IMO E
Asked: If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?
Last year: -
Let the Number of voters who voted for Revolutionary Party = r
Let the Number of voters who voted for Status Quo Party = s
Total voters who voted = r + s
This year: -
The Number of voters who voted for Revolutionary Party =1.1r
The Number of voters who voted for Status Quo Party = 1.05s
Total voters who voted = 1.1r + 1.05s = 1.08(r+s)
.02r = .03s
r = 1.5s
The Number of voters who voted for Revolutionary Party =1.1r = 1.1*1.5s = 1.65s
The Number of voters who voted for Status Quo Party = 1.05s
Total voters who voted = 1.65s + 1.05s = 2.7s
The fraction of voters voted Revolutionary this year = 1.65s / 2.7s = 165/270 = 11/18
IMO E
30 Apr 2023, 04:33
Kudos
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My approach
Last year:- R+S=100
this year:- 1.1R+1.05S=108
By Solving the both equations R=60 and S=40
Now this year Revolutionary Party got 1.1R votes which is 1.1R= 66
So fraction of voters voted Revolutionary this year= 66/108 = 11/18
Answer choice is E
Last year:- R+S=100
this year:- 1.1R+1.05S=108
By Solving the both equations R=60 and S=40
Now this year Revolutionary Party got 1.1R votes which is 1.1R= 66
So fraction of voters voted Revolutionary this year= 66/108 = 11/18
Answer choice is E
12 Jul 2025, 08:00
Kudos
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No. This will give you the % who voted for Revolutionary last year. The question is asking for this year, which is why we will plug in 2R=3S in the equation.
adamsmith2010
