In an election, the successful candidate secured 5,77,500 votes and his
nearest rival secured 3,48,700 votes. By what margin did the successful
candidate win? If 2580 votes were declard invalid. How many people cast their votes?

Answer

To solve the problem step by step, let's break it down into two parts: finding the margin of victory and calculating the total number of votes cast.

### Step 1: Calculate the Margin of Victory
1. **Identify the votes secured by the successful candidate and his nearest rival.**
- Successful candidate's votes = 577,500
- Nearest rival's votes = 348,700

2. **Calculate the margin by subtracting the votes of the nearest rival from the votes of the successful candidate.**
\[ \text{Margin} = \text{Votes of Successful Candidate} - \text{Votes of Nearest Rival} \]
\[ \text{Margin} = 577,500 - 348,700 \]
\[ \text{Margin} = 228,800 \]

### Step 2: Calculate the Total Votes Cast
1. **Identify the number of invalid votes.**
- Invalid votes = 2,580

2. **Calculate the total number of votes cast by adding the valid votes (the sum of the votes of both candidates) and the invalid votes.**
\[ \text{Total Valid Votes} = \text{Votes of Successful Candidate} + \text{Votes of Nearest Rival} \]
\[ \text{Total Valid Votes} = 577,500 + 348,700 \]
\[ \text{Total Valid Votes} = 926,200 \]

3. **Now, add the invalid votes to find the total votes cast.**
\[ \text{Total Votes Cast} = \text{Total Valid Votes} + \text{Invalid Votes} \]
\[ \text{Total Votes Cast} = 926,200 + 2,580 \]
\[ \text{Total Votes Cast} = 928,780 \]

### Final Answers
- The margin by which the successful candidate won is **228,800 votes**.
- The total number of people who cast their votes is **928,780**.

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