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Two-fifths of the voters promise to vote for P and the rest promise to vote for Q. Of these, on the last day, $15$% of the voters went back on their promise to vote for P and $25$% of voters went back of their promise to vote for Q, and P lost by 2 votes. Then the total number of voters is:

  1. $100$ 
  2. $110$ 
  3. $90$ 
  4. $95$
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1 Answer

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Assume  there were x voters in the city .

0.4x promised to vote for P(Two-fifths of the voters promise to vote for P) out of which 0.06x voted for Q(15% of two-fifth i.e. 15% of 0.4x)

0.6x promised to vote for Q( rest promise to vote for Q) out of which 0.15x voted for P(25% of rest i.e. 25% of 0.6x)

Total votes P got = 0.40x - 0.06x + 0.15x = 0.49x 
Total votes Q got = 0.60x + 0.06x - 0.15x = 0.51x 

As given in the question that  P lost by 2 votes

0.02x = 2 

 the total number of voters is : 100

Hence Option A is the Correct Answer.

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