In an election between two candidates, one got 55% of the total valid votes,…
2022
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was ______.
Answer: D. 2700 — ConceptOnly valid votes decide an election. When a fraction of all votes is invalid, Valid votes = Total votes × (1 − invalid fraction). In a two-candidate…
- A.
2500
- B.
2900
- C.
3100
- D.
2700
Attempted by 29 students.
Show answer & explanation
Correct answer: D
Concept
Only valid votes decide an election. When a fraction of all votes is invalid, Valid votes = Total votes × (1 − invalid fraction). In a two-candidate contest the candidates' valid-vote shares add up to 100%, so the other candidate's share = 100% − the first candidate's share, and a candidate's vote count = (that candidate's share) × (valid votes).
Application
Invalid votes are 20% of the total, so valid votes are 80% of the total: valid = 7500 × 80/100 = 6000.
One candidate took 55% of the valid votes, so the other candidate took the rest: 100% − 55% = 45% of the valid votes.
Votes for the other candidate = 45% of 6000 = 6000 × 45/100 = 2700.
Cross-check
The two candidates together hold all the valid votes: 55% of 6000 = 3300 and 45% of 6000 = 2700, and 3300 + 2700 = 6000, which is exactly the valid-vote count. This confirms 2700.