Two persons contested an election of Parliament . The winning candidate secured `57%` of the total votes polled and won by a majority of 42,000 votes. The number of total votes polled is

Options

A. 4,00,000
B. 5,00,000
C. 6,00,000
D. 3,00,000

Answer

To solve the problem, let's break it down step by step.

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

### Step 2: Calculate the votes received by the winning candidate
The winning candidate secured \( 57\% \) of the total votes. Therefore, the number of votes received by the winning candidate is:
\[ \text{Votes for winning candidate} = 0.57V \]

### Step 3: Calculate the votes received by the losing candidate
Since there are only two candidates, the losing candidate received the remaining votes. Thus, the votes received by the losing candidate is:
\[ \text{Votes for losing candidate} = V - 0.57V = 0.43V \]

### Step 4: Set up the equation based on the majority
The winning candidate won by a majority of \( 42,000 \) votes. This means the difference between the votes received by the winning candidate and the losing candidate is:
\[ 0.57V - 0.43V = 42,000 \]

### Step 5: Simplify the equation
Now, simplify the left side:
\[ 0.14V = 42,000 \]

### Step 6: Solve for \( V \)
To find \( V \), divide both sides by \( 0.14 \):
\[ V = \frac{42,000}{0.14} \]
\[ V = 300,000 \]

### Conclusion
The total number of votes polled is \( 300,000 \).

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