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?

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SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 05 Jul, 2024 Shift 4)

Answer 1

Given:

W = Winner, R1 = 1st runner-up, R2 = 2nd Runner-up, N = NOTA

Winner = 2 × R2

R1 = N + 900

R1 - R2 = 150

W + R1 + R2 + N = Total number of votes

W + R1 + R2 = 6 × N

Formula used:

R1 = R2 + 150

R2 = N + 750

W = 2 × (N + 750)

Calculation:

⇒ W = 2N + 1500

⇒ R1 = N + 900

⇒ R2 = N + 750

⇒ (2N + 1500) + (N + 900) + (N + 750) + N = Total number of votes

⇒ 5N + 3150 = Total number of votes

⇒ (2N + 1500) + (N + 900) + (N + 750) = 6N

⇒ 4N + 3150 = 6N

⇒ 2N = 3150

⇒ N = 1575

⇒ Total number of votes = 5 × 1575 + 3150

⇒ Total number of votes = 7875 + 3150

⇒ Total number of votes = 11025

∴ The total number of votes polled is 11025.

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