In an election between two candidates, 84%
In an election between two candidates, 84% of the registered voters cast their votes and 20% of the votes polled were found invalid. Winning candidate got 58% of the valid votes and won the election by a margin of 336 votes. How many voters were registered?
दो उम्मीदवारों के बीच हुए चुनाव में, पंजीकृत मतदाताओं में से 84% ने अपना वोट डाला। डाले गए वोटों में से 20% वोट अवैध पाए गए। विजयी उम्मीदवार को वैध वोटों का 58% प्राप्त हुआ और उसने 336 वोटों के अंतर से चुनाव जीत लिया। कुल कितने मतदाता पंजीकृत थे?
Detailed Solution & Logic
3125
Let total registered voters = N
Step 1: Votes cast
84% voted
Votes cast = 0.84N
Step 2: Valid votes
20% invalid ⇒ 80% valid
Valid votes = $0.8 \times 0.84N = 0.672N$
Step 3: Votes of candidates
Winner gets 58% of valid votes
So loser gets 42%
Difference = $(58 - 42)% = 16%$ of valid votes
So margin:
$0.16 \times 0.672N = 0.10752N$
Given margin = 336
So,
$0.10752N = 336$
Step 4: Solve for N
$N = \frac{336}{0.10752} = 3125$
Final Answer: 3125
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