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?

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??

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

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.