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
- If the list had 12,000 voters, 9,600 would vote and X's 12% lead would be 1,152 votes, not 1,440.
- (c) 9600
- 9,600 is not the size of the list; with 9,600 voters only 7,680 would vote and the margin would be about 922.
- (d) 5000
- With 5,000 voters only 4,000 would vote and the margin would be 480 votes, not 1,440.
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.