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

Let $x$ be the number of votes

• Number of votes $P$ was supposed to get $=0.4x$
• Number of votes $Q$ was supposed to get $=0.6x$

Now according to the given conditions,

• Number of votes $P$ got $=\frac{85}{100}(0.4x)+\frac{25}{100}(0.6 x)$
• Number of votes $Q$ has got $= \frac{75}{100}(0.6x)+\frac{15}{100}(0.4x)$

$Q-P=2$

$\implies \frac{75}{100}(0.6x)+\frac{15}{100}(0.4x)-\frac{85}{100}(0.4x)-\frac{25}{100}(0.6 x)=2$

$\implies 45x + 6x - 34x - 15x = 200$

$\implies x = 100$

Correct Option: A.

Comments

it should be Q – P =2

---

yes Q-P=2.

Answer 2

Ans a. 100

Exp:-

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

Comments

If no of voters not equal to 100 , your method fails

Answer 3

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 4

Let $V_P$, $V_Q$ be the total votes received by the candidate $P$ and $Q$ respectively and the total number of voters be $x$.

Now

$V_P=(40\%-40\%\times 15\%+60\%\times 25\%)x=\left(\frac{40}{100}-\frac{40}{100}\times\frac{15}{100}+\frac{60}{100}\times\frac{25}{100}\right)x=\frac{49x}{100}\\V_Q=(60\%+40\%\times 15\%-60\%\times 25\%)x=\left(\frac{60}{100}+\frac{40}{100}\times\frac{15}{100}-\frac{60}{100}\times\frac{25}{100}\right)x=\frac{51x}{100}$

 

According to the question finally,

$\begin{align} V_P &=V_Q-2\\ \Rightarrow V_Q-V_P &=2\\ \Rightarrow \frac{51x}{100}-\frac{49x}{100}&=2\\\ \Rightarrow \frac{2x}{100}&=2\\ \therefore x&=100\end{align}$

 

Therefore, the number of voters is $100$.

 

So the correct answer is A.

Answer 5

used the technique from paging and tlb acess. let total were x

for p = 0.40x

q=0.60x

15% of q = 0.60 * 0.15 x ; =0.09x

they have not voted for q. so

(0.60x-0.09x) - (0.40x+0.09x) = 2

0.02x=2

x=100

Comments

you could have answered in step 3 as 15% of q that is .09x cant be a fraction as they are voters so x is 100.

Answer 6

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$:A$