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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? 

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?  Correct Answer 100

Let; Total number of voters = X

Number of voters P was supposed to get = 0.4X

Number of voters Q was supposed to get =  0.6X

According to the given information;

Number of voters P got = 85/100 (0.4X) + 25/100 (0.6X)

Number of voters Q got = 75/100 (0.6X) + 15/100 (0.4X)

Q - P = 2

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

⇒ 50/100 (0.6X) - 70/100 (0.4X) = 2

⇒ 30X - 28X = 200

⇒ 2X = 200

⇒ X = 100

Hence, total number of voters are 100.

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