In an election two candidates participated. 10% voters did not vote. 11(1/9)% votes declared invalid and the winner got 75% of the valid votes. If he won by 2000 votes, find the number of voters in the voting list. 

Total numbers of voters be 100. Numbers of voters who voted (90%) = 90 Number of valid votes = 90 × 800/900 = 80 Winning candidate got 75% of valid votes = 75/100 × 80 = 60 Looser got = 80 – 60 = 20  Difference between winning and losing candidates votes = 2000 60 – 20 = 2000  40 = 2000 100 = (2000 )/(40 )×100  = 5,000   Alternate method: Let total number of voters = x 10% did not cast their votes , so votes polled = 90% & 100/9% of votes polled were invalid so Valid votes = x(90%  - 90%/9) = 80% of x  Winner gets 75 % So loser gets 25% So gap  = 50% of valid votes So now equation becomes x×80%×50%=2000 or x=5000