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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. $95$

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

So, no of voters=100

selected

let x be no of votes

no of votes P was supposed to get=0.4x

no of votes Q was supposed to get=0.6x

now acc to given condition

P has got=85/100(0.4x)+25/100(0.6 x)

Q has got 75/100(0.6x)+15/100(0.4x)

P-Q=2

75/100(0.6x)+15/100(0.4x)-85/100(0.4x)+25/100(0.6 x)=2

solving the equation we get

x=100

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
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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.
+1 vote
Ans -> A) 100

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.

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