There are two candidates $P$ and $Q$ in an election. During the campaign, $40\%$ of the voters promised to vote for $P,$ and rest for $Q.$ However, on the day of election $15\%$ of the voters went back on their promise to vote for $P$ and instead voted for $Q.$ $25\%$ of the voters went back on their promise to vote for $Q$ and instead voted for $P.$ Suppose, $P$ lost by $2$ votes, then what was the total number of voters?
Ans a. 100
Suppose no. Of voters =100
So Promised to vote P =40
Promised to vote Q=60
Then 15% of the voter promised to vote p went back and voted for Q = 15% of 40= 6
Rest out of 40 voted for P=34
similarly, 25% of 60 voted for P= 15
Rest out of 60 voted for P=45
So voted for P= 49
So voted for Q=51 voters
Difference between votes 51-49=2
So, no of voters=100
let x be no of votes
no of votes P was supposed to get=0.4x
no of votes Q was supposed to get=0.6x
now acc to given condition
P has got=85/100(0.4x)+25/100(0.6 x)
Q has got 75/100(0.6x)+15/100(0.4x)
solving the equation we get
Let the number of voters be 100.
Then, the number of candidates which promised to vote for P = 40
and the no. of candidates promised to vote for Q = 100 – 40 = 60
According to question,
15% of 40 = 6 voters went back on their promise to vote for
P and instead voted for Q.
and 25% of 60 = 15 voters went back on their promise to vote
for Q and instead voted for P.
Number of Votes for P = 40 – 6 + 15 = 49
and Number of Votes for Q = 60 + 6 – 15 = 51
Difference of Votes = 51 – 49 = 2.
Also P lost by 2 Votes.
Number of Voters were 100.
This link may be useful for understanding it.
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