In an election, one of the two candidates gets `40%` votes and loses by `100` votes. Total number of votes is

Options

A. 500
B. 400
C. 600
D. 1000

Answer

To solve the problem, we will follow these steps:

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

### Step 2: Calculate the votes received by each candidate
- The first candidate received \( 40\% \) of the total votes, which can be expressed as:
\[ \text{Votes for Candidate 1} = 0.4X \]
- The second candidate received the remaining votes, which is \( 60\% \) of the total votes:
\[ \text{Votes for Candidate 2} = 0.6X \]

### Step 3: Set up the equation based on the information given
According to the problem, the first candidate lost by \( 100 \) votes. This means that the difference in votes between the two candidates is \( 100 \):
\[ \text{Votes for Candidate 2} - \text{Votes for Candidate 1} = 100 \]
Substituting the expressions we found:
\[ 0.6X - 0.4X = 100 \]

### Step 4: Simplify the equation
Now, simplify the left side:
\[ 0.2X = 100 \]

### Step 5: Solve for \( X \)
To find \( X \), divide both sides by \( 0.2 \):
\[ X = \frac{100}{0.2} = 500 \]

### Conclusion
The total number of votes in the election is \( 500 \).

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