Question

Three candidates "A", "B", "C" participated in an election. "A" gets 40% of the votes more than "B". "C" gets 20% votes more than "B". "A" also overtakes "C" by 4000 votes. If 90% voters voted and no invalid or illegal votes were cast, then what will be the number of voters in the voting list?

• A. 72000
• B. 80000
• C. 70000
• D. 78500

Answer 1

The Correct Option is B

Let's denote the number of votes received by candidates "B", "A", and "C" as B, A, and C respectively. We can express A and C's votes in terms of B's votes:

• A receives 40% more votes than B: \( A = B + 0.4B = 1.4B \)
• C receives 20% more votes than B: \( C = B + 0.2B = 1.2B \) 

The problem states that candidate A overtakes candidate C by 4000 votes:

• \( A = C + 4000 \) or equivalently \( 1.4B = 1.2B + 4000 \)
• Solving for B, we get: \( 1.4B - 1.2B = 4000 \Rightarrow 0.2B = 4000 \Rightarrow B = \frac{4000}{0.2} = 20000 \)

Now that we know B=20000, we can calculate the total votes:

• Total votes obtained by A: \( A = 1.4 \times 20000 = 28000 \)
• Total votes obtained by B: B=20000
• Total votes obtained by C: \( C = 1.2 \times 20000 = 24000 \)
• Total number of votes cast: \( A + B + C = 28000 + 20000 + 24000 = 72000 \)

Given that 90% of voters on the list voted, the total number of voters in the voting list is:

• \( 0.9 \times \text{Total Voters} = 72000 \)
• Solving for the total number of voters gives: \(\text{Total Voters} = \frac{72000}{0.9} = 80000 \)

Therefore, the number of voters in the voting list is 80000.