In an election, a voter has choices to vote for one candidate out of three candidates. There is also an option ‘None Of The Above’ (NOTA) to reject all candidates. The three candidates get votes that are 6 times NOTA. The winner gets votes that are twice the second runner-up’s votes. The first runner-up gets 900 votes more than NOTA and defeats the second runner-up by 150 votes. What is the total number of votes polled?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 11025.
NOTA = N; Winner = W; First runner up = R1; Second runner up = R2
R1 = N + 900 .....(1)
R1 = R2 + 150
⇒ N + 900 = R2 + 150
⇒ R2 = N + 750 .....(2)
W = 2R2 = 2N + 1500 .....(3)
So, (2N + 1500) + (N + 900) + (N + 750) = 6N
⇒ 4N + 3150 = 6N
⇒ 2N = 3150
⇒ N = 3150/2 = 1575
Total votes = N + 4N + 3150 = 1575 + (4 × 1575) + 3150 = 11025