In an election between two candidates A and B, the number of valid votes…
2024
In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 20% of the total number of votes polled. If 15% of the votes polled were invalid and a total of 9200 votes were polled, then how many valid votes did B get ?
- A.
2990
- B.
3150
- C.
4830
- D.
3560
Attempted by 176 students.
Show answer & explanation
Correct answer: A
Answer: 2990 valid votes for candidate B.
Step 1: Compute total valid votes. Total polled = 9200 and 15% are invalid, so valid = 85% of 9200 = 0.85 × 9200 = 7820.
Step 2: Compute the lead. The number of votes by which A exceeds B = 20% of total polled = 0.20 × 9200 = 1840.
Step 3: Set up and solve equations using A + B = 7820 and A − B = 1840.
Add the equations: 2A = 7820 + 1840 = 9660 → A = 9660 ÷ 2 = 4830.
Find B: B = 7820 − A = 7820 − 4830 = 2990.
Common mistake: Taking 20% of valid votes instead of 20% of total polled. The problem explicitly states the excess is 20% of the total number of votes polled.