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28 Jan 2022, 05:45
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Difficulty:
95%
(hard)
Question Stats:
19% (02:25) correct
81%
(02:22)
wrong
based on 48
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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
Are You Up For the Challenge: 700 Level Questions
A. 1,250
B. 3,500
C. 3,600
D. 4,000
E. 6,000
Are You Up For the Challenge: 700 Level Questions
28 Jan 2022, 07:50
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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
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
Updated on: 28 Jan 2022, 11:43
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.
Last edited by sujoykrdatta on 28 Jan 2022, 11:43, edited 1 time in total.
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Bunuel
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
