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A, B, and C participated in an election, in which 10% of total voters didn’t cast their votes and the exact number of votes was disqualified as they were invalid. A won the election. The difference between the vote share of B and C was 12.5% of the valid votes. If A won by 2400 votes and got 50% of valid votes, find out the total voters in the voting list.

A, B, and C participated in an election, in which 10% of total voters didn’t cast their votes and the exact number of votes was disqualified as they were invalid. A won the election. The difference between the vote share of B and C was 12.5% of the valid votes. If A won by 2400 votes and got 50% of valid votes, find out the total voters in the voting list. Correct Answer 16000

GIVEN:

Number of participants = 3

Percentage of voters who didn’t participate = 10% of total votes

Votes disqualified = 10% of total votes

Winning vote share = 2400 votes

TERMINOLOGY USED:

The difference in vote share is known as winning votes.

COMMON MISTAKE:

A won with 2400 votes, 2400 votes is a difference between A and B’s vote share not a difference between A and C’s vote share. (i.e. the difference between 1st’s vote share and 2nd’s vote share and not of 1st and 3rd )

A won by x votes is often misguided as A got x votes.

CALCULATIONS:

Total valid votes = Total votes – votes disqualified – Voters didn’t participate

⇒ Total valid votes = 100% – 10% – 10% = 80% of total votes

Let, the total voters be 100x.

⇒ Total valid votes = 80% of 100x = 80x.

A’s votes = 50% of valid votes = 50% of 80x = 40x.

⇒ B’s votes – C’s votes = 12.5% of 80x = 10x      ----(i)

⇒ B’s votes + C’s votes = (A + B + C)’s votes – A’s votes

⇒ B’s votes + C’s votes = 80x – 40x = 40x      ----(ii)

Solving equation(i) and equation (ii),

⇒ B’s votes = 25x

⇒ C’s votes = 15x

A won with 2400 votes,

⇒ A’s votes – B’s votes = 2400

⇒ 40x – 25x = 2400

⇒ 15x = 2400

⇒ x = 2400/15 = 160

⇒ Total votes = 100x = 100 × 160 = 16000

∴ The total number of voters is 16000 in the voting list.

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