In an election between two candidates, the candidate who won r... | Mathematics MCQ | Examoogle

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MathematicsPrevious Year Paper 2024

In an election between two candidates, the candidate who won received 1854 votes, whereas the candidate who lost received 618 votes. What percentage of the total number of votes received by the two candidates went in favour of the winning candidate?

60%

75%

70%

80%

Correct Answer

📐 MA • Math Ratio MethodMathematicsPrevious Year Paper 2024

Option B

75%

Quick Summary:

Notice the ratio: $1854 \div 618 = 3$ . The winning candidate has $3$ parts and the loser has $1$ part. Total parts = $3+1=4$ . Percentage = $\frac{3}{4} \times 100 = 75\%$ .

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📐MAMath SolutionRatio Method

📋 Given

Winning candidate votes = 1854, Losing candidate votes = 618

🔢 Formula Used

Percentage=WinningVotesTotalVotes×100\text{Percentage} = \frac{\text{Winning} \text{Votes}}{\text{Total} \text{Votes}} \times 100Percentage=TotalVotesWinningVotes​×100

⚡ Exam Hall Shortcut / Speed Trick

Notice the ratio: $1854 \div 618 = 3$ . The winning candidate has $3$ parts and the loser has $1$ part. Total parts = $3+1=4$ . Percentage = $\frac{3}{4} \times 100 = 75\%$ .

⚠️ Common Student Trap / Pitfall

Adding only the winning votes to the denominator instead of the total votes ( $1854 + 618$ ), or failing to realize the ratio is exactly $3:1$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate Total Votes

To find the total number of votes, add the votes received by both candidates: $1854 + 618 = 2472$ .

1854+618=24721854 + 618 = 24721854+618=2472

Set up Percentage Calculation

The percentage of votes in favour of the winner is the winning votes divided by the total votes, multiplied by $100$ .

Percentage=18542472×100\text{Percentage} = \frac{1854}{2472} \times 100Percentage=24721854​×100

Solve the Fraction

Simplify the fraction $\frac{1854}{2472}$ . Since $1854 = 3 \times 618$ and $2472 = 4 \times 618$ , the ratio is $\frac{3}{4}$ .

18542472=34=0.75\frac{1854}{2472} = \frac{3}{4} = 0.7524721854​=43​=0.75

Final Percentage

Convert the ratio to a percentage by multiplying by $100$ : $0.75 \times 100 = 75\%$ .

0.75×100=75%0.75 \times 100 = 75\%0.75×100=75%

✅

B is correct because the winning candidate received $1854$ out of a total of $2472$ votes, which equates to exactly $75\%$ .

Core Concepts Used

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Percentage Ratio and Proportion Basic Arithmetic

💡 EXAM TIP

Always look for integer ratios between numbers in data interpretation questions to simplify calculations; here $1854$ is exactly $3$ times $618$ .

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