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 !5% 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?
A) 100
B) 110
C) 90
D) 95
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7
comments:
manoj
said...
Let the number of voters = x. the number of candidates which promised to vote for P = .4x the no. of candidates promised to vote for Q = x-.4x=.6x According to given condition, 15% of .4x voters went back on their promise to vote for P and instead voted for Q. so: .4x * 15/100=.06x 25% of 60 voters went back on their promise to vote for Q and instead voted for P. so: .6x * 25/100=.15x the total no. of votes for P = .4x–.06x+.15x= .49x
so as the total no. of Votes for Q =.6x+.06 – .15x = .51x
Difference of Votes = .51x – .49x = 2
.02x=2 x=2/.02 x=100 so there will be hundred voters Also P lost by 2 Votes.
Option is A. Let the question be solved in this way, supposing the total number of voters in village be x. As 40% promised for P but only 25% turned back , for Q they promised 60% but only 35% votes are polled for him and remaining 25% for P. So, P=25+25, Q=15+35 Now , the count is 50% each and now let X be the percentage of votes after poll, as per analogy X+X+2=100% or X=49% and other won by 51% out of 100% which means 100 votes polled.
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7 comments:
Let the number of voters = x.
the number of candidates which promised to vote for P = .4x
the no. of candidates promised to vote for Q = x-.4x=.6x
According to given condition,
15% of .4x voters went back on their promise to vote for P and instead voted for Q.
so:
.4x * 15/100=.06x
25% of 60 voters went back on their promise to vote for Q and instead voted for P.
so:
.6x * 25/100=.15x
the total no. of votes for P = .4x–.06x+.15x= .49x
so as the total no. of Votes for Q =.6x+.06 – .15x = .51x
Difference of Votes = .51x – .49x = 2
.02x=2
x=2/.02
x=100
so there will be hundred voters
Also P lost by 2 Votes.
⇒ Number of Voters were 100
Option is A.
Let the question be solved in this way, supposing the total number of voters in village be x.
As 40% promised for P but only 25% turned back , for Q they promised 60% but only 35% votes are polled for him and remaining 25% for P.
So, P=25+25, Q=15+35
Now , the count is 50% each and now let X be the percentage of votes after poll, as per analogy X+X+2=100% or X=49% and other won by 51% out of 100% which means 100 votes polled.
A only
it is option A 100
answer:a
@ Manoj and Karthik Reddy (Winner rs 50 mobile recharge free)
Thanks for your detailed answer. You both solved the problem with different approaches. All the best for your GATE preparation. Please contact me with your mobile number at examsavvy@gmail.com
a is the answer
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