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Math Help - Voter numbers promising to vote for each candidate

  1. #1
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    Voter numbers promising to vote for each candidate

    the last GATE exam i got a Q. like this, how can i solve it in the proper way?


    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



    the An. (C) 90
    Last edited by CaptainBlack; February 16th 2011 at 10:37 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ajanthakumar View Post
    the last GATE exam i got a Q. like this, how can i solve it in the proper way?


    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



    the An. (C) 90
    Let $$N be the number of voters. Then interpret the question to give the number that voted for each candidate:

    N_p=(0.4-0.15+0.25)N

    N_q = N- N_p

    Then you are told that N_q-N_p=2

    Except that this is impossible since N_p=N_q=0.5N. So the wording is wrong, it should read "15% of the voters who had promised to vote for P went back on their promise and voted for Q, and 25% of the voters who had promised to vote for Q went back on their promise and voted for P"

    Then:

    N_p=0.4N - (0.15)(0.4)N+ (0.25)(0.6)N=0.49N

    But now the answer is N=100

    CB
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