GATE2011 AG: GA-4

Question

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?

• A. $100$
• B. $110$
• C. $90$
• D. $95$

Comments

Wording of language is really important so read carefully use of instead.

Answer 1

Ans -> A) 100

Answer 2

Let Total number of voters be $100$

Actions	Votes of P	Votes of Q
During the campaign,40% of the voters promised to vote for P, and rest for Q.	40	60
15% of the voters went back on their promise to vote for P and instead voted for Q	40 - (15% of 40) = 40 -6 = 34	60 + (15% of 40) = 60 + 6 = 66.
25% of the voters went back on their promise to vote for Q and instead voted for P	34 + (25% of 60) = 34 + 15 = 49	66 - (25% of 60) = 66 -15 = 51

Given: P lost by 2 votes i.e Q-P = 2.

In our assumption also Q-P = 51 -49 =2.

$\therefore$ Option A. $100$ is the correct answer.

Answer 3

Total number of voters$=x$

Initially$ :P=40\%\ of\ x,Q=60\%\ of\ x$

However, on the day of election 15% of the voters went back on their promise to vote for P and instead voted for Q.

$15\%\ of\ 40\%\ of\ x=Q$

$\therefore 85\%\ of\ 40\%\ of\ x=P$

25% of the voters went back on their promise to vote for Q and instead voted for P.

$25\%\ of\ 60\%\ of\ x=P$

$\therefore 75\%\ of\ 60\%\ of\ x=Q$

 

P lost by 2 votes

$\Rightarrow(15\%\ of\ 40\%\ of\ x+75\%\ of\ 60\%\ of\ x)-(25\%\ of\ 60\%\ of\ x+85\%\ of\ 40\%\ of\ x)=2$

$\Rightarrow \frac{5100x}{10000}-\frac{4900x}{10000}=2$

$\Rightarrow 200x=20000$

$\Rightarrow x=100$

Correct Answer$:A$

Answer 4

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.

reference: https://www.allinterview.com/showanswers/160596/two-candidates-p-q-election-during-campaign-40-voters-promised-vote-rest-however.html