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

Answer

To solve the problem, we need to determine the total number of votes polled in the election. Let's denote the total votes polled as \( V \).

1. **Identify the votes secured by the winning candidate:**
The winning candidate secured 57% of the total votes. Therefore, the votes secured by the winning candidate can be expressed as:
\[ \text{Votes for winning candidate} = 0.57V \]

2. **Identify the votes secured by the losing candidate:**
Since there are only two candidates, the votes secured by the losing candidate will be the remaining percentage of the total votes. Thus, the votes secured by the losing candidate can be expressed as:
\[ \text{Votes for losing candidate} = V - \text{Votes for winning candidate} = V - 0.57V = 0.43V \]

3. **Set up the equation using the majority:**
The problem states that the winning candidate won by a majority of 42,000 votes. The majority can be expressed as the difference between the votes secured by the winning candidate and the votes secured by the losing candidate:
\[ \text{Majority} = \text{Votes for winning candidate} - \text{Votes for losing candidate} \]
Substituting the expressions we found:
\[ 0.57V - 0.43V = 42,000 \]

4. **Simplify the equation:**
Simplifying the left side gives:
\[ 0.14V = 42,000 \]

5. **Solve for \( V \):**
To find the total votes polled \( V \), divide both sides of the equation by 0.14:
\[ V = \frac{42,000}{0.14} \]
Calculating this gives:
\[ V = 300,000 \]

Thus, the total number of votes polled is **300,000**.