Question:
In an election between two candidates, 80% of the voters cast their votes, out of which 5% votes were declared invalid. A candidate got 13680 votes which were 60% of the valid votes. Then, what is the total number of voters enrolled in that election?
A32,000
B30,000
C28,000
D35,000
Answer:
B. 30,000
Explanation:
60% of valid votes = 13680
Total number of voters enrolled in that election was 100x.
voters cast their votes = 80x
Number of valid votes = 95% of 80x = 76x
60% of 76x = 13680
⇒ 228x / 5 = 13680
⇒ x / 5 = 60
⇒ x = 300
The total number of votes enrolled in that election was 100x = 30,000
Alternate method
Invalid votes = 0.05 × 0.8x = 0.04x
Valid votes = 0.8x - 0.04x = 0.76x
According to question
13680 = 0.76x × 0.6
⇒ x = 30000