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In a village 70% cast their votes in an election. Only two candidates A and B contested the election. A won the election by 400 votes. Had A received 12.5% less votes, the resulted would have been tie. How many registered voters in village?
Asked by Shivam Last Modified
Pawan Kumar Yadav
Tutor
Answer: 8571
Let the number of votes received by A and B be a and b, respectively.
Then, b = a - 400
Also, a*87.5/100 = b
a - 400 = 875a/1000
⇒ 1000a - 400000 = 875a
⇒ 125a = 400000
⇒ a = 3200
And, b = 3200 - 400 = 2800
Thus, Total votes casted = 3200 + 2800 = 6000 Number of registered voters = 6000*100/70 = 8571.43
But since it's the number of registered voters, which must be a whole number, so there are 8571 registered voters.
read lessPalak Kanti Maitra
I have a degree in Mechanical Engineering I have conducted over 12000 online sessions on Math. durin
Suppose candidate A gets x votes and candidate B gets y votes. Then -
Equation 1 : x - y = 400 ...... (1)
Had A received 12.5% less votes, the resulted would have been tie. Therefore-
x - 25 / 2 × 1 / 100 x = y
Which on simplification is 200 x - 25 x = 200 y
OR 175 x = 200 y
Or 175 x - 200 y = 0 ....... (2)
Simplifying 1 & 2 , we get
Candidate A(????) got 3200 votes &
Candidate B (??) got 2800 votes.
ANS : Total registered voters = 3200+2800=6000
{70 per cent cast their votes- is not required for solving the sum. It's to distract. Best to avoid the information in this sum}
from Subhash Sir??
read lessLet us assume that B got 'x' number of votes.
B got x number of votes.But, when A got (x + 400)/8 less votes then votes that B got = x + (x + 400)/8
= (8x + x + 400)/8
New number of votes that B got = (9x + 400)/8 ........(2)
Now,there is tie when A would have got 12.5 % less votes.
So, (1) = (2)
(7x + 2800)/8 = (9x + 400)/8
56x + 22400 = 72x + 3200
56x - 72x = 3200 - 22400
- 16x = - 19200
x = 19200/16
x = 1200
Number of that B got = 1200
And number of votes that A got = 1200 + 400 = 1600
Total votes casted = 1200 + 1600 = 2800
This is only 70 % of the total registered votes.
Number of registered voters in the village = (2800*100)/70
= 4000
Deepika Agrawal
Interested to teach to class 1 to 5 , 6 to 10 , 11&12
Let us assume that B got 'x' number of votes.
Then A got x + 400 number of votes.
When if A gets 12.5 % fewer votes then the result would have been a tie.
So, according to the question = {(x + 400)*12.5}/100
= (x + 400)/8
New number of votes that A got = (x + 400) - (x + 400)/8
= (8x + 3200 - x - 400)8
New number of votes that A got = (7x + 2800)/8 ...........(1)
Now, originally B got x number of votes.
But, when A got (x + 400)/8 less votes then votes that B got = x + (x + 400)/8
= (8x + x + 400)/8
New number of votes that B got = (9x + 400)/8 ........(2)
Now,there is tie when A would have got 12.5 % less votes.
So, (1) = (2)
(7x + 2800)/8 = (9x + 400)/8
56x + 22400 = 72x + 3200
56x - 72x = 3200 - 22400
- 16x = - 19200
x = 19200/16
x = 1200
Number of that B got = 1200
And number of votes that A got = 1200 + 400 = 1600
Total votes casted = 1200 + 1600 = 2800
This is only 70 % of the total registered votes.
Now,
Number of registered voters in the village = (2800*100)/70
= 4000
Total registered voters in the village are 4000
Case 1: Let the total number of votes gained by B be "x".
Therefore,the votes gained by A will be "x+400".
Total number of votes gained by A and B put together is, therefore,
"(2*x)+400"....…......(1)
Case 2: When A gets 12.5% less votes,there would have been a tie.
Therefore, combined votes gained by both A and B is,
"(2*0.875*(x+400))"........…..(2)
Equating (1) and (2), we get
2*(x+200)=2*(0.875*(x+400)
0.125*x= (400*0.875)-200
X=150/0.125=1200
Number of people who voted= (2*1200)+400
=2800
If "y" is the registered number of voters, 0.7*"y" =2800
Therefore, y=(2800/0.7)=4000.
So total number of registered voters=4000.
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