In an election between two candidates A and B, 15% of the voters did not cast their votes, 20% of the votes cast were declared invalid. The winning candidate got 8262 votes, which were 54% of the total valid votes.

Statement I: The candidate who was defeated got votes from 31.28% of the total voters in the list.

Statement II: The number of valid votes was 15500.

Which of the above statements is/are correct?

Correct option is D

Given:

• 15% voters did not vote → 85% voted
• 20% of cast votes were invalid → 80% valid votes
• Winning candidate got 8262 votes = 54% of valid votes
• We need to verify Statement I and Statement II.

Solution:

Valid votes = (8262 × 100) ÷ 54
Total votes cast = Valid votes ÷ 0.80
Total voters = Total votes cast ÷ 0.85
Defeated candidate votes = Valid votes – 8262
% of total voters = (Defeated candidate votes ÷ Total voters) × 100

Step 1: Find total valid votes

Valid votes = (8262 × 100) ÷ 54 = 15300

So, Statement II: “The number of valid votes was 15500” → Incorrect
(Actual valid votes = 15300)

Step 2: Total votes cast = 15300 / 0.80 = 19125

Step 3: Total voters = 19125 / 0.85 = 22500

Step 4: Defeated candidate votes = 15300 – 8262 = 7038

Step 5: Percentage of total voters = (7038 ÷ 22500) × 100 = 31.28%

So, Statement I: “The candidate who was defeated got votes from 31.28% of total voters” → Correct

Final Answer:

(d) I only