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
I. 2y2- 37y + 143 = 0
II. 2x2+ 15x – 143 = 0
I.8(x+3)+ 8(-x)=72
II. 5(y+5)+ 5(-x)=150
I. x2 – 13x + 40 = 0
II. 2y2 – 15y + 13 = 0
I. (2x-3)3+ 1/((2x-3)³)=2
II. 4y²+(y+8)^2= 157
I. 17x² - 26x – 16 = 0
II. 17y²- 26y + 9 = 0
I. 20y² - 13y + 2 = 0
II. 6x² - 25x + 14 = 0
I. 6x2 + 23x + 10 = 0
II. 2y2 - 3y - 5 = 0
I. 3x2 – 16x + 21 = 0
II. y2 – 13y + 42 = 0
I. 2y2 + 31y + 99 = 0
II. 4x2 + 8x – 45 = 0
I. 2x2– 5x – 63 = 0
II. 2y2– 7y – 72 = 0