Percentages Question 1 - CAT 2023
In an election, there were four candidates, and 80% of the registered voters cast their votes.
- One candidate received 30% of the votes cast.
- The remaining votes were distributed among the other three candidates in the ratio 1 : 2 : 3.
If the winner received 2512 votes more than the candidate with the second-highest votes, then the number of registered voters was:
Step-by-Step Explanation
Assume the total number of registered voters is 100x.
Since 80% voted, the total votes cast are:
80x
One candidate received 30% of the votes cast:
30% × 80x = 24x
The remaining votes are:
80x − 24x = 56x
These are divided in the ratio 1 : 2 : 3, so the three candidates receive:
56x / 6
112x / 6
168x / 6 = 28x
Thus, the winner gets 28x votes, while the second-highest candidate gets 24x votes.
Given,
28x − 24x = 2512
4x = 2512
x = 628
Therefore, the total number of registered voters is:
100x = 100 × 628 = 62,800
Hence, the correct answer is Option D.
💡 FundaMakers Tip: When percentages and ratios appear together, first assume a convenient total (like 100x). Then convert percentages into actual values before applying the given conditions.