20% of the voters did not cast their vote in an election between two…
2025
20% of the voters did not cast their vote in an election between two candidates. 20% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 5120 votes. Find the total number of voters enrolled on the voter list.
Answer: B. 100000 — Solution: Let the total number of voters be N. 20% did not vote, so votes polled = 80% of N = 0.8N. 20% of the polled votes were invalid, so valid votes = 80%…
- A.
250000
- B.
100000
- C.
200000
- D.
175000
Attempted by 49 students.
Show answer & explanation
Correct answer: B
Solution:
Let the total number of voters be N.
20% did not vote, so votes polled = 80% of N = 0.8N.
20% of the polled votes were invalid, so valid votes = 80% of 0.8N = 0.8 × 0.8N = 0.64N.
The successful candidate got 54% of valid votes = 0.54 × 0.64N = 0.3456N. The other candidate got 46% = 0.46 × 0.64N = 0.2944N.
Majority = difference = 0.3456N − 0.2944N = 0.0512N. This is given as 5120.
So 0.0512N = 5120, hence N = 5120 / 0.0512 = 100000.
Quick verification: votes polled = 80% of 100000 = 80000; valid votes = 80% of 80000 = 64000; successful = 54% of 64000 = 34560; opponent = 29440; majority = 34560 − 29440 = 5120, which matches.