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CAT 2022Slot 2QAQues & Sol

ArithmeticEasy

Question

In an election, there were four candidates and 80% of the registered voters casted 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

Options

Solution

1. Concept Used

  • Topic: Ratio and Proportion combined with Percentages
  • Formula: $$\text{Votes for candidate} = \text{Fraction of total casted votes} \times \text{Total casted votes}$$

2. Calculation

Let the total number of registered voters be ( 100x ).

Since 80% of registered voters cast their votes, the total casted votes ( = 80x ).

Candidate A received 30% of casted votes: $$\text{Votes}_A = \frac{30}{100} \times 80x = 24x$$

The remaining votes distributed among the other three candidates (B, C, D) in ratio ( 1:2:3 ): $$\text{Remaining votes} = 80x - 24x = 56x$$

The sum of ratio parts ( = 1 + 2 + 3 = 6 ), so: $$\text{Votes}_B = \frac{1}{6} \times 56x = \frac{56x}{6}$$ $$\text{Votes}_C = \frac{2}{6} \times 56x = \frac{112x}{6}$$ $$\text{Votes}_D = \frac{3}{6} \times 56x = \frac{168x}{6} = 28x$$

Now let's list all four candidates' votes:

  • Candidate A: ( 24x )
  • Candidate B: ( \approx 9.33x )
  • Candidate C: ( \approx 18.67x )
  • Candidate D: ( 28x )

Winner = Candidate D with ( 28x ) votes. Second highest = Candidate A with ( 24x ) votes.

Given that the winner received 2512 more votes than the second-highest candidate: $$28x - 24x = 2512$$ $$4x = 2512$$ $$x = 628$$

Therefore, the total number of registered voters: $$= 100x = 100 \times 628 = 62800$$

3. Solution

Answer = Option D ✅

The total number of registered voters is 62,800.