In an election, two candidates Rahul and Karan are contesting.
During campaigning, 60% of the voters promised to vote for Rahul and the rest promised to vote for Karan. However, on the day of the election, 10% of the voters who had promised to vote for Rahul switched their vote to Karan, and 20% of the voters who had promised to vote for Karan switched their vote to Rahul. If Rahul won by 360 votes, how many people voted in the election?
A 1500
B 3000
2000
D
2500

Let's denote the total number of voters as \( N \).

### Step 1: Initial distribution of votes
- 60% of the voters promised to vote for Rahul: \( 0.6N \)
- 40% of the voters promised to vote for Karan: \( 0.4N \)

### Step 2: Vote switching on election day
- 10% of the voters who had promised to vote for Rahul switched to Karan: \( 0.1 \times 0.6N = 0.06N \)
- 20% of the voters who had promised to vote for Karan switched to Rahul: \( 0.2 \times 0.4N = 0.08N \)

### Step 3: Final votes for Rahul and Karan
- Final votes for Rahul:
  \[
  \text{Rahul's votes} = \text{Original votes} - \text{Switched votes to Karan} + \text{Votes switched from Karan}
  \]
  \[
  = 0.6N - 0.06N + 0.08N = 0.62N
  \]
- Final votes for Karan:
  \[
  \text{Karan's votes} = \text{Original votes} - \text{Switched votes to Rahul} + \text{Votes switched from Rahul}
  \]
  \[
  = 0.4N - 0.08N + 0.06N = 0.38N
  \]

### Step 4: Rahul's winning margin
We are told that Rahul won by 360 votes, so the difference in their votes is:
\[
0.62N - 0.38N = 360
\]
\[
0.24N = 360
\]
\[
N = \frac{360}{0.24} = 1500
\]

### Answer:
The total number of voters is 1500, so the correct option is **A. 1500**.

Would you like more details on any step or have any other questions?

Here are 5 related questions for further exploration:
1. How would the outcome change if 30% of Karan's voters switched to Rahul instead?
2. What would be the result if the initial promises were split evenly between Rahul and Karan?
3. How many voters would Rahul lose if 20% of his voters switched to Karan?
4. If only 5% of voters switched sides, what would be the winning margin?
5. How many votes would Karan need to win if he gained an additional 100 votes before switching?

**Tip:** Understanding how percentage-based changes affect total numbers is crucial for solving election problems. Always break down the steps logically.

In an election, two candidates Rahul and Karan are contesting. During campaigning, 60% of the voters promised to vote for Rahul and the rest promised to vote for Karan. However, on the day of the election, 10% of the voters who had promised to vote for Rahul switched their vote to Karan, and 20% of the voters who had promised to vote for Karan switched their vote to Rahul. If Rahul won by 360 votes, how many people voted in the election? A 1500 B 3000 C 2000 D 2500

Solve an election problem where Rahul wins by 360 votes after voter switching. The problem involves percentage calculations, linear equations, and vote distribution analysis. Suitable for Grades 8-10.

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