Two candidates X and Y contested an election. 80% of voters cast their vote and there were no invalid votes. There was no NOTA (None of the above) option. X got 56% of the votes cast and won by 1440 votes. What is the total number of voters in the voters list?
- (a) 15000 ✓ UPSC's answer
- (b) 12000
- (c) 9600
- (d) 5000
Why the answer is (a)
• Let the total number of voters be V. Since 80% of voters cast their votes, the total votes cast is 0.8V.
• Candidate X received 56% of the votes cast, so Candidate Y received the remaining 44% (100% - 56%).
• The difference in their vote shares is 56% - 44% = 12% of the total votes cast.
• This 12% difference corresponds to the winning margin of 1440 votes, so 0.12 * (0.8V) = 1440.
• Solving for V: 0.096V = 1440, which gives V = 1440 / 0.096 = 15000.
• Therefore, the total number of voters in the list is 15000, matching option (a).
Why the other options are wrong
- (b) 12000
- 12000 is incorrect because it results from miscalculating the effective percentage of total voters or ignoring the 80% turnout factor in the final division.
- (c) 9600
- 9600 is incorrect because it represents the number of votes actually cast (0.8 * 12000) or a miscalculation of the base population.
- (d) 5000
- 5000 is incorrect because it is significantly lower than the required total to generate a 1440-vote margin from a 12% difference of the 80% turnout.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.