In an election between two candidates, 10% of the voters in the voter list did not cast their vote, whereas 10% of the votes cast were found to be invalid. The winning candidate got 56% of the valid votes and won the election by a margin of 1,458 votes. What is the total number of voters enrolled in the voter list?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 2)

Answer 1

Given:

10% of the voters did not cast their vote and 10% of the polled vote were found invalid.

The winning candidate got 56% of the valid votes and won the election by a margin of 1,458 votes.

Concept Used:

The percentage is calculated based on 100 i.e. 100 is the base

40% means 40 out of 100

Calculation:

Let, the total enrolled voters be x

10% did not cast a vote means cast or polled vote = 9x/10

10% vote is invalid

That means valid vote = (90/100) × (9x/10)

⇒ 81x/100

The winning candidate got 56% of the polled vote means the looser got (100 – 56) = 44% vote

Winer candidate got total {(56/100) × (81x/100)} vote

And the looser candidate got {(44/100) × (81x/100)} vote

Accordingly,

{(56/100) × (81x/100)} - {(44/100) × (81x/100)} = 1458

⇒ (81x/100) × {(56 – 44)/100} = 1458

⇒ (81 × 12)x/10000 = 1458

⇒ x = (1458× 10000)/(81 × 12)

⇒ x = 15000

∴ Total 15000 voters enrolled in the voter list.

Shortcut Trick

Total voters = 1458 × (100/90) × (100/90) × 100\(56 - 44) = 15000