In an election, 2 candidates participate in which the winner gets 60% of the total votes, and he wins the election by 2000 votes. Find the total number of votes in the election.

Options

A. 3200
B. 6400
C. 10000
D. 13250

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the total number of votes
Let the total number of votes in the election be represented by \( X \).

### Step 2: Determine the votes received by each candidate
According to the problem, the winner receives 60% of the total votes, while the losing candidate receives the remaining 40%. Therefore:
- Votes received by the winner = \( 0.6X \)
- Votes received by the loser = \( 0.4X \)

### Step 3: Set up the equation based on the winning margin
The winner wins the election by a margin of 2000 votes. This can be expressed as:
\[ \text{Votes received by winner} - \text{Votes received by loser} = 2000 \]
Substituting the expressions from Step 2, we get:
\[ 0.6X - 0.4X = 2000 \]

### Step 4: Simplify the equation
Now, simplify the left side of the equation:
\[ 0.2X = 2000 \]

### Step 5: Solve for \( X \)
To find \( X \), divide both sides of the equation by 0.2:
\[ X = \frac{2000}{0.2} = 10000 \]

### Step 6: Conclusion
The total number of votes in the election is \( 10000 \).

### Final Answer
The total number of votes in the election is **10,000**.

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