Arithmetic-3 (GATE-2011)

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
Solution follows here:

Solution:

Let the total votes be ‘x’.

The following table depicts the stats of P and Q:

	P	Q
Earlier Promise	0.4x	0.6x
Day of election	0.4x - (0.15)(0.4)x + (0.25)(0.6)x = 0.4x-0.06x+0.15x = 0.49x	0.6x+(0.15)(0.4)x-(0.25)(0.6)x = 0.6x+0.06x-0.15x = 0.51x

Finally P got ‘0.49x’  votes and Q got  ‘0.51x’  votes

=> P lost by 0.02x votes
But its given that P lost by 2 votes

=> 0.02x = 2 => x = 2/0.02 = 200/2 = 100

Answer (A)