Question

​In a village, 70% registered voters cast their votes in the 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 results would have been tie. How many registered voters are there in the village?

Answer 1

Solution:-
Let us assume that B got 'x' number of votes.
Then A got x + 400 number of votes.
When if A get 12.5 % less 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
Answer.

Answer 2

12.5= 1/8

8 se 7 ho jaega second time

8 : 6
7 : 7

2 = 400
14 = 2800...this is 70%

Now..30%= 6= 1200

2800+1200= 4000