Averages , Ratio and Proportion Question 4 - CAT 2022
In an election, there were four candidates and 80% of the registered voters cast their votes. One of the candidates received 30% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was:
Step-by-Step Explanation
- Analyze the distribution of cast votes:
Let the total number of cast votes be 100c.
Candidate 1 received 30% of 100c = 30c votes.
Remaining votes pool = 100c − 30c = 70c votes
- Distribute the remaining pool among the other candidates:
The remaining three candidates split the 70c votes in the proportion 1 : 2 : 3 (which sums to 6 parts).
Candidate 2 = (1/6) × 70c = 11.67c
Candidate 3 = (2/6) × 70c = 23.33c
Candidate 4 = (3/6) × 70c = 35c
- Identify the winner and runner-up:
Comparing all four allocations (30c, 11.67c, 23.33c, 35c), Candidate 4 is the clear winner (35c) and Candidate 1 is the runner-up (30c).
Vote Difference = 35c − 30c = 5c
Given that this difference equals 2512 votes:
5c = 2512
100c = 2512 × 20 = 50240 cast votes
- Calculate the number of registered voters:
Since only 80% of registered voters cast their votes:
Registered Voters = 50240/0.80 = 62800
Correct Option: D
💡 FundaMakers Tip:
When handling ratios that don't divide cleanly (like 70 into 6 parts), keep your variables in fractional form or scale your initial assumption. If you assume the total number of cast votes is 600c instead of 100c, Candidate 1 gets 180c and the remaining 420c splits into a clean 70c : 140c : 210c layout. The difference becomes 210c − 180c = 30c = 2512, which gives the answer without any decimals.