Questions :
In an election, 70% of eligible voters cast their votes. Of these votes, 5% were declared invalid. The winning candidate received 15,960 votes, which was exactly 40% of the total valid votes. What was the total number of eligible voters in the election?
Options :
- 50,000
- 52,500
- 60,000
- 67,500
correct answer : c)
Explanation :
Let the total number of eligible voters be x.
Votes cast = 70% of x
= 0.70x
Valid votes = 95% of votes cast
= 0.70x × (95/100)
= 0.665x
The winning candidate received 40% of the valid votes.
So,
0.665x × (40/100) = 15,960
⇒ 0.266x = 15,960
⇒ x = 15,960 / 0.266
⇒ x = 60,000
Therefore, the total number of eligible voters in the election was 60,000.
Hence, the correct answer is option (c) 60,000. The values 50,000, 52,500, and 67,500 do not satisfy the given voting percentages and vote counts, and are therefore incorrect.