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?

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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... read more

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.

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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 ... read more

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??

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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)/8New number of votes that A got = (x + 400) - (x + 400)/8= (8x + 3200 - x - 400)8New... read more

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

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Comments

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... read more

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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Comments

Let 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 %... read more

Let 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

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