Question : In an election, 2% of persons enrolled in the voter list did not participate and 500 votes were invalid. Two candidates A and B fought the election and A defeated B by 200 votes. If 43% of the persons enrolled in the voter list cast their votes in favour of A, then what is the number of the total cast votes?
Option 1: 2450
Option 2: 2800
Option 3: 3000
Option 4: 3250
Correct Answer: 2450
Solution :
Let the number of persons enrolled in the voter list be $x$.
The 2% of the enrolled persons did not participate in the election, which implies that 98% of the total enrolled persons did participate.
The total number of cast votes = $0.98x$
Included, 500 votes were invalid,
The total number of valid votes = $0.98x - 500$
Candidate A received 43% of the total enrolled votes = $0.43x$
Since A defeated B by 200 votes, B must have received = $0.43x - 200$ votes.
$0.98x - 500 = 0.43x + (0.43x - 200)$
⇒ $0.98x - 500 = 0.86x - 200$
⇒ $0.12x = 300$
⇒ $x = \frac{300}{0.12} = 2500$
The total number of cast votes $=0.98x = 0.98 \times 2500 = 2450$
Hence, the correct answer is 2450.
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