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8 votes
8 votes

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?

  1. $100$
  2. $110$
  3. $90$
  4. $95$
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8 Answers

Best answer
18 votes
18 votes

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.

edited by
4 votes
4 votes

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

3 votes
3 votes

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.

2 votes
2 votes
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
Answer:

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