Question : In an election between two candidates, 30% of the electorate did not cast their votes. 20% of the votes polled were found invalid. The winning candidate got 64% of the valid votes and won by a majority of 3136 votes. Find the number of voters enrolled in the voter list.
Option 1: 20000
Option 2: 25000
Option 3: 24000
Option 4: 30000
Correct Answer: 20000
Solution : Given: 30% of voters did not cast their votes 20% are declared as invalid Winner gets = 64% of valid votes Calculation: Let the total number of voters in the voting list be 100% According to the question, 30% of voters did not cast their votes = 100 of 30% = 30 Remaining votes = (100 - 30)% = 70% 20% are declared as invalid = 20% of 70% = 14% Valid votes = 70% - 14% = 56% Winner candidate gets 64% of valid votes = 64% of 56% The loser candidate gets 36% of valid votes = 36% of 56% According to the question, 56% of 64% - 56% of 36% = 3136 ⇒ 56% × $(\frac{28}{100})$ = 3136 ⇒ 1% = $\frac{(3136 × 100)}{(28 × 56)}$ ⇒ 1% = 200 ⇒ 100% = 20,000 Hence, the correct answer is 20,000.
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