Vinod and Sanjay were fighting against each other for the post of a village Pradhan. Sanjay got 47.5% votes and lost the election by 270 votes. How many votes did Vinod get (assuming that all the villagers participated in the voting)?
Pradhan Election Vote Calculation
This problem involves calculating the number of votes Vinod received in a village Pradhan election. We are given the percentage of votes Sanjay received and the margin by which he lost the election. We need to find Vinod's vote count, assuming all villagers participated in the voting.
Vote Percentages Analysis
First, let's understand the vote distribution based on the information provided:
- Sanjay received 47.5% of the total votes.
- Since Sanjay lost the election, Vinod must have received the remaining votes, which means Vinod secured more than 50% of the votes.
- The total percentage of votes must add up to 100%.
Therefore, Vinod's percentage of votes can be calculated as:
Vinod's Percentage = \( 100\% - \text{Sanjay's Percentage} \)
Vinod's Percentage = \( 100\% - 47.5\% = 52.5\% \)
Total Votes Calculation from Margin
We are told that Sanjay lost the election by 270 votes. This difference in votes represents the difference between Vinod's percentage and Sanjay's percentage.
- The difference in vote percentage between Vinod and Sanjay is:
Percentage Difference = \( \text{Vinod's Percentage} - \text{Sanjay's Percentage} \)
Percentage Difference = \( 52.5\% - 47.5\% = 5\% \)
This 5% difference corresponds to the 270 votes by which Sanjay lost.
Let 'T' be the total number of votes cast in the election. We can set up the equation:
\( 5\% \text{ of } T = 270 \)
To find the total votes (T), we convert the percentage to a decimal and solve:
\( \frac{5}{100} \times T = 270 \)
\( 0.05 \times T = 270 \)
\( T = \frac{270}{0.05} \)
\( T = \frac{270}{\frac{5}{100}} = 270 \times \frac{100}{5} \)
\( T = 270 \times 20 \)
\( T = 5400 \)
So, the total number of votes cast in the election was 5400.
Vinod's Winning Votes Calculation
Now that we know the total number of votes (5400) and Vinod's percentage of votes (52.5%), we can calculate the number of votes Vinod received.
Vinod's Votes = \( 52.5\% \text{ of Total Votes} \)
Vinod's Votes = \( 0.525 \times 5400 \)
Calculation:
\( 0.525 \times 5400 = 2835 \)
Alternatively, we could first calculate Sanjay's votes and then add the margin:
Sanjay's Votes = \( 47.5\% \text{ of } 5400 \)
Sanjay's Votes = \( 0.475 \times 5400 = 2565 \)
Vinod's Votes = Sanjay's Votes + Margin of Loss
Vinod's Votes = \( 2565 + 270 = 2835 \)
Both methods confirm that Vinod received 2835 votes.
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