In a village, three people contested for the post of Village Pradhan.

Question

In a village, three people contested for the post of Village Pradhan. Due to their own interest, all the voters voted and no one vote was invalid. The losing candidate got 30% votes. What could be the minimum absolute margin of votes by which the winning candidate led by the nearest rival, if each candidate got an integral percent of votes?

A) 4

B) 2

C) 1

D) 3

E) None of these

Show Answer

Official Answer

B

A) 4

B) 2

C) 1

D) 3

E) None of these

rajatchopra1994 · Answer

Explanation:

saidurrahman  , This is very easy question Sub 600 level
Let Voters of the village are 100
three people contested for the post of Village Pradhan, out of one got 30% votes i.e. 30 votes.
So total votes left 70
Now Between 2 people, who contested win by an integral margin & it should be minimum

So, One can get 36 Votes and other will get 34.

margin is = 36-34 = 2

IMO-B

Hope you understand.

Regards,
Rajat Chopra

nityakaul02 · Answer

I can not understand how the integral margin is divided

stne · Answer

nityakaul02

The question is asking the minimum number of votes by which the winner could have won from the person who came second.

Let total votes be 100 
Given that the person who lost got 30 , now remaining 70 votes

if remaining two people both got 35 votes then we have a draw. So the winner must get minimum 36 votes to have a majority of votes and win then the other person will get 70-36 =34 votes  
 
Hence the minimum vote by which the winner can win from the nearest rival is 2.

Can you make the difference of votes between and winner and runner up less than 2? No.

Hence 2 is the most  minimum margin  by which the winner can win.

Ans-B

Hope it's clear.

kkang98 · Answer

Can the margin not be 1 vote?

Say there are 50 voters; if 30% vote for the losing candidate, they get 15 votes. 
That leaves 70% or 35 votes to be divided among the top two candidates. The smallest margin of victory would be when one gets 36% of the votes and the other gets 34% of the votes, or 50(.36)=18 votes, and 50(.34)=17 votes.

What am I missing?

stne · Answer

kkang98 , 
You have to find the smallest margin in terms of number of votes ( integers) and NOT in terms of percentage.
In terms of percentage one could also divide the remaining percentage in 35.1% and 34.9%, however in these case number of votes won't be an integer.

Hence instead of finding narrowest margin in terms of percentage try finding narrowest margin in terms of number of votes and see if you can get 1 vote margin!

Choose an easy number so that the winner and runner up can have equal number of votes and then try finding the margin.

Hope this helps.

urmi760 · Answer

stne 
If total number of voters are 10, then margin should be 1.

stne · Answer

urmi

Not possible 
Please show your working how you arrived at 1.

urmi760 · Answer

stne 
Total number of voters = 10
One candidate got 30% votes = 3votes
Out of remaining 7 votes, winner will get 4votes (40%) and other will get 3 votes (30%).
It's not mentioned that no two candidates can have same number of votes.

Isn't this correct?

stne · Answer

urmi760 ,

Remember there is a winner, nearest rival and person who got 30% votes.
We have to find the narrowest margin between winner and nearest rival.

I believe the phrase "  led  by the nearest rival " means " nearest rival is leading from among the non winners. Hence person who got 30% votes and nearest rival cannot have same number of votes.

Maybe question could have been better framed to avoid such ambiguity.

Try tagging an expert and see if they can help.

Hope this helps to some extent.

ayushbhardwaj · Answer

My answer is coming out to be 1.
What if we assume 50 people to be voting, in that case:

Losing candidate will get 15 votes (30%), winning candidate will get 18 votes (36%) and the third person will get 17 votes (34%).
Minimum absolute margin in such a case will be 18-17 = 1.

ronakm94 · Answer

IMO, if there is no mention of how many voters there actually are or any further information to justify an answer of 2, then the minimum absolute margin will be 1 as 1 is a possibility. For example, with 50 voters, the minimum absolute margin is 1 vote.

v12345 · Answer

ayushbhardwaj 
 ronakm94

Absolute margin of votes here is asked in the way of percentage,
so if 50 votes, 1 vote is margin
Percentage margin = 1/50 * 100 % = 2%

Hence, OA is (B).

luisdicampo · Answer

Deconstructing the Question

There are   3   candidates.

The losing candidate got   30\%   of the votes.

So the other two candidates together got

70\%

We need the minimum possible absolute margin of votes between the winner and the nearest rival, given that each candidate received an integral percent of votes.

Step-by-step

To minimize the winner's lead over the nearest rival, split the remaining  70\%  as evenly as possible.

The equal split would be

35\% 	ext{ and } 35\%

but then there would be no winner.

So the closest possible unequal integral split is

36\% 	ext{ and } 34\%

Thus the minimum percentage lead is

36-34=2\%

Now convert this into absolute votes.

Using a total of  100  votes gives

30,\ 34,\ 36

which are all integers and satisfy the conditions.

So the absolute margin is

36-34=2

Answer B

In a village, three people contested for the post of Village Pradhan.

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In a village, three people contested for the post of Village Pradhan.

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