(Q1)In an election, there were only two candidates. one of the candidates secured 40% of votes and is defeated by the other candidate by 298 votes. The total number of votes polled is.

Solution: Let total votes=100x

Now,

60x-40x=298

=>20x=298

∴ x=298/20

=14.6

Total votes=100x

=100×14.6

=1460 votes Ans.

Rough:

100x×(40/100)

=40x

100x×(60/100)

=60x

(Q2)In an election between two candidates, the candidate getting 60% of the votes polled, is elected by a majority of 14000 votes . The number of votes polled by the winning candidate is.

Solution:

60x-40x=14000

20x=14000

∴ x=14000/20

=700

Number of votes polled by the winning candidate=60x

=60×700

=42000 votes Ans.

(Q3)8% of the votes in an election did not cast their votes. In this election, there only two candidates. The winner by obtaining 48% of the total votes defeated his contestant by 1100 votes. The total number of voters in the election was.

Solution:

Now,

48x-44x=1100

=>4x=1100

∴ x=1100/4

Total number of voter=100x

=100×(1100/4)

=27500 voters Ans

Concept:[8% of the voters in an election did not cast their votes, it means only 92% voter cast their votes now winner candidates secure 48% votes ∴ Loser candidate=92%-48%=44%]

(Q4)In an election between two candidates, One got 55% of the total valid votes,20% of the votes were invalid. If the total number of votes was 7500,the number of valid votes that the other candidate got, was.

Solution: Total number of votes =7500

20% invalid votes

i.e 7500×(20/100)

=1500 invalid votes.

now valid votes=7500-1500=6000 votes

one candidate got 55% of the total valid votes

i.e 6000×(55/100)

=3300 votes

2nd candidate got=6000-3300

=2700 votes Ans.

(Q5)10% of the voters did not cast their vote in an election between two candidates.10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes. The numbers of voters enrolled on the voter list.

Solution: Let the numbers of voters enrolled on the voter list=100x

Now,

81x×(54/100)-81x×(46/100)=1620

81x[(54/100)-(46/100)]=1620

∴ x=(1620×100)/(81×8)

=250

The numbers of voters enrolled on the voter list=100x

=100×250

=25000 Ans.

Rough:

10% did not cast their votes

i.e 100x×(10/100)

=10x voter did not cast vote

∴ casting vote=100x-10x=90x

10% invalid votes of 90x

i.e 90x(10/100)

=9x

∴ valid votes=90x-9x=81x