Three candidates A,B and C contested an election. Out of the total votes list `25%` did not vote and `6.66%` votes polled were invalid. C got 2450 valid votes, which were `40%` more than that of B. If A Got only `40%` of the total votes, then who is the winner?

Options

A. A
B. B
C. C
D. Can't be determined

Answer

To solve the problem step by step, we will first determine the total number of votes, then calculate the votes received by each candidate, and finally identify the winner.

### Step 1: Determine the total number of votes
Let the total number of votes be \( V \).

According to the problem, 25% of the total votes did not vote. Therefore, the percentage of votes that were cast is:
\[ 100\% - 25\% = 75\% \]
So, the number of votes cast is:
\[ 0.75V \]

### Step 2: Calculate the number of invalid votes
It is given that 6.66% of the votes polled were invalid. Therefore, the number of invalid votes is:
\[ 6.66\% \text{ of } 0.75V = 0.0666 \times 0.75V = 0.04995V \]

### Step 3: Calculate the number of valid votes
The number of valid votes is the total votes cast minus the invalid votes:
\[ \text{Valid votes} = 0.75V - 0.04995V = 0.70005V \]

### Step 4: Determine the votes received by candidate B
We know that candidate C received 2450 valid votes, which is 40% more than the votes received by candidate B. Let the votes received by B be \( b \). Then:
\[ 2450 = b + 0.4b = 1.4b \]
To find \( b \):
\[ b = \frac{2450}{1.4} = 1750 \]

### Step 5: Determine the votes received by candidate A
It is given that candidate A received 40% of the total votes \( V \):
\[ \text{Votes for A} = 0.40V \]

### Step 6: Calculate the total valid votes
From Step 3, we have:
\[ 0.70005V = A + B + C \]
Substituting the values we have:
\[ 0.70005V = 0.40V + 1750 + 2450 \]
Combining the votes:
\[ 0.70005V = 0.40V + 4200 \]

### Step 7: Solve for total votes \( V \)
Rearranging the equation:
\[ 0.70005V - 0.40V = 4200 \]
\[ 0.30005V = 4200 \]
\[ V = \frac{4200}{0.30005} \approx 13996.67 \text{ (approximately 14000)} \]

### Step 8: Calculate votes for A
Now we can find the votes for A:
\[ \text{Votes for A} = 0.40 \times 14000 = 5600 \]

### Step 9: Summary of votes
- Votes for A = 5600
- Votes for B = 1750
- Votes for C = 2450

### Step 10: Determine the winner
Comparing the votes:
- A: 5600
- B: 1750
- C: 2450

Candidate A has the highest votes.

### Conclusion
The winner of the election is **Candidate A**.

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