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.

Solution

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