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In a village 60% votes were cast in an election. A and B were the cont

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Bunuel
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In a village 60% votes were cast in an election. A and B were the cont [#permalink] New post   28 Jan 2022, 05:45
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In a village 60% votes were cast in an election. A and B were the contestants. A won by 600 votes. If B had got 40% more votes, there would have been a tie between them. What was the number of recognized voters in the village ?

A. 1,250
B. 3,500
C. 3,600
D. 4,000
E. 6,000


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gmatophobia
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Re: In a village 60% votes were cast in an election. A and B were the cont [#permalink] New post   28 Jan 2022, 07:50
Let the number of eligible votes = x

Number of eligible votes who casted a vote=\( \frac{60 }{ 100 }x \)= 0.6 x

Lets assume that the number of votes in favor of B = y

number of votes in favor of A = 0.6x - y

Given

Votes (A) - Votes (B) = 600

( 0.6x - y ) - y = 600

2y = 0.6x - 600

y = 0.3x - 300 ---------- Eq. 1

If B had got 40% more votes

number of votes in favor of B = 1 + \( \frac{40 }{ 100 }y\) = 1.4 y

number of votes in favor of A = 0.6x - 1.4y

Given : 0.6x - 1.4y = 1.4 y

2.8 y = 0.6x

\( \frac{x }{ y }\) = \( \frac{ 3 }{ 14 }\) ---------- Eq. 2

Substituting the value of y from Eq.2 to Eq.1

\( \frac{ 3 }{ 14 } * x\) = (0.3*x) - 300

Simplifying we get x = 3500
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In a village 60% votes were cast in an election. A and B were the cont [#permalink] New post   Updated on: 28 Jan 2022, 11:43
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Bunuel wrote:
In a village 60% votes were cast in an election. A and B were the contestants. A won by 600 votes. If B had got 40% more votes, there would have been a tie between them. What was the number of recognized voters in the village ?

A. 1,250
B. 3,500
C. 3,600
D. 4,000
E. 6,000

Are You Up For the Challenge: 700 Level Questions


We know that if B had got 40% more votes, there would have been a tie between A and B
=> A = 1.4B

Since A won by 600 votes: A - B = 600
=> 1.4B - B = 600
=> B = 1500
Thus, we have:
A + B = 2.4B = 3600

Thus, 60% of the votes cast = 3600
=> Number of recognized voters = 3600 x 100/60 = 6000

Answer E
This is assuming that the votes of B increased without affecting the votes of A.
The statement says that had B's votes increased by 40% - it doesn't say from where the increase happens. It may be that some of those who hadn't voted, now voted and that increased B's share. Note that 2400 people hadn't voted and for B's share to increase by 40%, B needs only 600 more votes.



Possibility 2:
Had the increase in the number of votes of B happened at the expense of A, we have:

Increased number of votes of B = B + 0.4B = 1.4B
Decreased number of votes of A = A - 0.4B
Since there is a tie: A - 0.4B = 1.4B
=> A = 1.8B

Since A won by 600 votes: A - B = 600
=> 1.8B - B = 600
=> 0.8B = 600
=> B = 750
Thus, we have:
A + B = 2.8B = 2100

=> 60% of voters = 2100
=> Number of voters = 2100 x 100/60 = 3500
Answer B

Originally posted by sujoykrdatta on 28 Jan 2022, 10:03.
Last edited by sujoykrdatta on 28 Jan 2022, 11:43, edited 1 time in total.
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In a village 60% votes were cast in an election. A and B were the cont [#permalink] New post   Updated on: 28 Jan 2022, 11:29
sujoykrdatta wrote:
Bunuel wrote:
In a village 60% votes were cast in an election. A and B were the contestants. A won by 600 votes. If B had got 40% more votes, there would have been a tie between them. What was the number of recognized voters in the village ?

A. 1,250
B. 3,500
C. 3,600
D. 4,000
E. 6,000

Are You Up For the Challenge: 700 Level Questions


We know that if B had got 40% more votes, there would have been a tie between A and B
=> A = 1.4B

Since A won by 600 votes: A - B = 600
=> 1.4B - B = 600
=> B = 1500
Thus, we have:
A + B = 2.4B = 3600

Thus, 60% of the votes cast = 3600
=> Number of recognized voters = 3600 x 100/60 = 6000

Answer E


sujoykrdatta - Sir, I had question on your approach.

In the solution you've shared,

The number of votes in favor of A = A

The number of votes in favor of B = B

Therefore, A - B = 600

Had B received 40% more votes, in that scenario you have equated A = 1.4B

Question that I have: Doesn't the 40% extra vote that B now receives reduces an equal number that candidate 'A' will receive. However you have kept the number (A) as constant.

The reason I think the number of votes candidate A receive will be fewer than 'A' is to keep the total constant (60% of the total population).

Sharing my thoughts based on which I solved the problem -

We know that the total votes casted is 60% of the entire population. So, the increase in the number for one candidate (B in this case),would decrease an equal amount of votes from the other candidate (A in this case) so that the total remains constant.

For example out of 100 people, 60 cast their vote.

A - 30 votes
B - 30 votes

Now if B were to receive an additional 10% (i.e. 3 more votes) of the votes received, then an equal amount would be reduced from A's share to keep the total constant.

Therefore the distribution that I assumed -

A - 27 votes
B- 33 votes



Please let me know if my understanding is flawed.

Originally posted by gmatophobia on 28 Jan 2022, 11:06.
Last edited by gmatophobia on 28 Jan 2022, 11:29, edited 2 times in total.
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In a village 60% votes were cast in an election. A and B were the cont [#permalink] New post   28 Jan 2022, 11:27
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AbhiroopGhosh wrote:
sujoykrdatta wrote:
Bunuel wrote:
In a village 60% votes were cast in an election. A and B were the contestants. A won by 600 votes. If B had got 40% more votes, there would have been a tie between them. What was the number of recognized voters in the village ?

A. 1,250
B. 3,500
C. 3,600
D. 4,000
E. 6,000

Are You Up For the Challenge: 700 Level Questions


We know that if B had got 40% more votes, there would have been a tie between A and B
=> A = 1.4B

Since A won by 600 votes: A - B = 600
=> 1.4B - B = 600
=> B = 1500
Thus, we have:
A + B = 2.4B = 3600

Thus, 60% of the votes cast = 3600
=> Number of recognized voters = 3600 x 100/60 = 6000

Answer E


sujoykrdatta - Sir, I had question on your approach.

In the solution you've shared,

The number of votes in favor of A = A

The number of votes in favor of B = B

Therefore, A - B = 600

Had B received 40% more votes, in that scenario you have equated A = 1.4B

Question that I have: Doesn't the 40% extra vote that B now receives reduces an equal number that candidate 'A' will receive. However you have kept the number (A) as constant.

The reason I think the number of votes candidate A receive will be fewer than 'A' is to keep the total constant (60% of the total population).

Sharing my thoughts based on which I solved the problem -

We know that the total votes casted is 60% of the entire population. So, the increase in the number for one candidate (B in this case),would decrease an equal amount of votes from the other candidate (A in this case) so that the total remains constant.

For example out of 100 people, 60 cast their vote.

A - 30 votes
B - 30 votes

Now if B were to receive an additional 10% (i.e. 3 more votes) of the votes received, then an equal amount would be reduced from A's share to keep the total constant.

Therefore the distribution that I assumed -

A - 27 votes
B- 33 votes



Please let me know if my understanding is flawed.



Excellent question.

The statement says that had B's votes increased by 40% - it doesn't say from where the increase happens. It may be that some of those who hadn't voted, now voted and that increased B's share.
Note that 2400 people hadn't voted and for B's share to increase by 40%, B needs only 600 more votes.
However, there is a slight ambiguity, and I think it would have better to mention that A's votes hadn't changed when B's votes increased.


Solving your case: Case 2:
Assuming that the increase in the number of votes of B happened at the expense of A, we have:

Increased number of votes of B = B + 0.4B = 1.4B
Decreased number of votes of A = A - 0.4B
Since there is a tie: A - 0.4B = 1.4B
=> A = 1.8B

Since A won by 600 votes: A - B = 600
=> 1.8B - B = 600
=> 0.8B = 600
=> B = 750
Thus, we have:
A + B = 2.8B = 2100

=> 60% of voters = 2100
=> Number of voters = 2100 x 100/60 = 3500
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Re: In a village 60% votes were cast in an election. A and B were the cont [#permalink] New post   28 Jan 2022, 12:40
According to the question,
140B/100=A
A:B=>7:5
(7-5)=2 unit is 600 votes
12 unit is 3600

So, 60% is 3600
100% is 6000

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Re: In a village 60% votes were cast in an election. A and B were the cont [#permalink]
28 Jan 2022, 12:40
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