in a village ,78./. votes were cast in an election.A and B were the contestants.B won by 1800 votes .if A had got 30./. more votes ,there would have been a tie between them.find the number of recognised voters in the village ?
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Let the total number of recognised voters be 78x. (since the number has to be a positive integer)
B won by 1800 votes
Therefore B=A+1800 --> (1)
We know the total number of people is 78x
Then A+B= 78x --> (2)
from (1) and (2)
78x - A = A + 1800
A = 39x + 900
if A had received 30% more votes then A' would have A + 30*A/100
A'= 1.3 A votes
= 1.3 * (39x + 900)
this value = B'
in (2) it is given A+B=78x
{since A'=B' ; A'+B'= 2A'}
2*1.3*(39x + 900) = 78x
x=7800
B won by 1800 votes
Therefore B=A+1800 --> (1)
We know the total number of people is 78x
Then A+B= 78x --> (2)
from (1) and (2)
78x - A = A + 1800
A = 39x + 900
if A had received 30% more votes then A' would have A + 30*A/100
A'= 1.3 A votes
= 1.3 * (39x + 900)
this value = B'
in (2) it is given A+B=78x
{since A'=B' ; A'+B'= 2A'}
2*1.3*(39x + 900) = 78x
x=7800
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