Math Help - Voter numbers promising to vote for each candidate

1. 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

2. Originally Posted by ajanthakumar
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