Elections

Algebra Level 2

Three candidates X, Y, Z contested in an election. Out of the total votes on a voter list 25% did not vote and 6.66% were invalid votes. Z got 2450 valid votes which is 40% more than that of Y. If X got only 40% of total votes , then who won the elections?

Tie Z Y X

3 solutions

Deepak Gowda
Jun 17, 2014

Let the total voters be 100%

25% did not caste their vote implies 75% voters participated in elections.

out of 75% voters 6.66% are invalid, remaining voters are approximately 68%.

X gets 40% of remaining valid votes. Thus X is the winner.

The demonstration is not complete.

Leonblum Iznotded - 2 years, 10 months ago

Leonblum Iznotded
Jul 25, 2018

Let us call T the total number of electors, voting or not, invalid or valid.

_ ** who _	_ % _	_ votes ** _
_no vote _	_ 25 _	_ 0,25T _
_ invalid _	_ 0,0666 _	_ 0,0666T _
_ Z _	_ _	_ 1,4Y = 2450 _
_ Y _	_ _	_ 2450/1,4 =1750 _
_ X _	_ _	_ 0,4T _
_ Total _	_ 100 _	_ T _

Z is 2450 votes and is 1,4Y (Y+40%Y=1,4Y) ; so Y=2450/1,4=1750

The total of votes is T = 0,25T + 0,0666T +2450+1750+0,4T

So T(1-0,25-0,0666-0,4)=4200

T=4200/0,2834 =14 820

X=0,4T=5928 ("X got only 40% of total votes" not "valid votes")

X, being superior (strictly) to Y, to Z, to invalid votes, X is the winner.

(many wonder what would do the political power if the number of blank suffrage were superior to any candidate ... ?)

James Wilson
Dec 27, 2017

Let T be the total number of votes. Assume X got all the invalid votes (worst case scenario for X). This means the number of valid votes that X got is $0.4T-0.0666T=0.3333T=X$ . Also, $Z=1.4Y=2450$ , so $Y=\frac{2450}{1.4}=1750$ . The votes that X,Y, and Z got total to 75% of the total number of votes. That is $0.4T+2450+1750=0.75T$ . Solving this results in $T=12000$ . This means that, in the worst case scenario, X receives 4000 valid votes (as well as all the invalid votes). So, X is the winner.

Elections

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