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

Hint:

Write A and C as multiples of B, then use the given difference to solve for B.

Answer 1

The Correct Option is B

To find the total number of voters in the voting list, let's analyze the given data step-by-step. 

1. Let the number of votes obtained by candidate "B" be \(x\).
2. According to the problem, candidate "A" gets 40% more votes than "B". Therefore, the votes for "A" will be: \(A = x + 0.4x = 1.4x\).
3. Candidate "C" receives 20% more votes than "B". Thus, the votes for "C" will be: \(C = x + 0.2x = 1.2x\).
4. It is also given that "A" overtakes "C" by 4000 votes. Thus, we have: \(1.4x - 1.2x = 4000\).
5. Simplifying the above equation gives: \(0.2x = 4000\)
6. Solving for \(x\), we have: \(x = \frac{4000}{0.2} = 20000\).
7. This means candidate "B" received 20000 votes.
8. The total number of votes cast, which accounts for 90% of the total voters, is: \(A + B + C = 1.4x + x + 1.2x = 3.6x\)
9. Substituting \(x = 20000\) into \(3.6x\), we get: \(3.6 \times 20000 = 72000\).
10. Since these 72000 votes correspond to 90% of the total number of voters, the total number of voters on the list is: \(\frac{72000}{0.9} = 80000\).

Hence, the total number of voters in the voting list is 80000.

Answer 2

Step 1: Write A and C in terms of B.  
"A" gets 40% more votes than "B", so \(A = 1.4B\). "C" gets 20% more votes than "B", so \(C = 1.2B\). 

Step 2: Use the given difference between A and C. 
We are told \(A - C = 4000\). Substituting: \(1.4B - 1.2B = 4000\), so \(0.2B = 4000\), giving \(B = 20000\). 

Step 3: Find A, C and the total votes cast. 
Then \(A = 1.4 \times 20000 = 28000\) and \(C = 1.2 \times 20000 = 24000\). Total votes cast \(= A + B + C = 28000 + 20000 + 24000 = 72000\). 

Step 4: Scale up from 90% to the full voting list. 
Since no invalid votes were cast, these 72000 votes are 90% of the total voting list. So the full list has \(72000 / 0.9 = 80000\) voters. 

Final Answer: 
The voting list has 80000 voters. \[ \boxed{80000} \]